







Factoring a quadratic 
20180402 

From Billy: I need help factoring the following question:
4x(squared) 10x +16. Answered by Penny Nom. 





Multiplies and factors 
20180224 

From Lil: Is a multiple the same as a factor? Answered by Penny Nom. 





A question about perfect squares 
20180204 

From Jolyn: Find the smallest possible value of a whole number m if 648x m is a perfect square Answered by Penny Nom. 





GCD 
20171125 

From A student: Suppose a,b, c are integers such that gcd(a,b)=gcd(a,c)=1. Show that gcd(a,bc)=1. Answered by Penny Nom. 





Abstract algebra 
20171125 

From A student: Suppose a,b, c are integers such that gcd(a,b)=gcd(a,c)=1. Show that gcd(a,bc)=1. Answered by Penny Nom. 





Scale factor 
20171103 

From Hannah: I do not understand it...... What is the scale factor for 9 cenimeters = 1 meter Answered by Penny Nom. 





Factors 
20170816 

From Gemma: Why do 315 and 525 have the same number of factors? Answered by Penny Nom. 





Factorials 
20170727 

From dinesh: Is there any shortcut formula for multiply series numbers.
like
1x2x3x4x5.......x100 =? Answered by Penny Nom. 





Baseball Cards 
20170420 

From Raquel: A minor league baseball team gave away baseball cards to each person entering the stadium. One group receives 28 baseball cards. A second group received 68 baseball card. If each person entering the stadium receive the same number of cards, what was the greatest possible number of baseball cards that each person could have received? Answered by Penny Nom. 





Solve 3x^219x14=0 for x 
20170315 

From nick: I'm an 8th grader and am quite confused with this equation:
3x^219x14=0
The answer is:
2/3 , 7
But I'm not sure how to solve for it. Answered by Penny Nom. 





A scale factor 
20160413 

From tonya: What is the scale factor for the two figures regular octagon with 15 and 9 written in decimal form Answered by Penny Nom. 





The remainder theorem 
20160327 

From Pratyasha: A quadratic polynomial when divide by x+2 leaves a remainder of 1 and when divided by x1 leaves a remainder of 4. What will be the remainder if it is divided by (x+2)(x1)? Answered by Penny Nom. 





An exercise with factorials 
20160207 

From vidhi: find the value of n: (11/2) (22/3) (33/4)...(1515/16) = n!/16 Answered by Penny Nom. 





A limit of a rational function 
20160116 

From selvamani: F (x) = x^3+3x^29x2 / x^3x6 and limit x tends to 2, f (x) exist then limit x tends to 2, f (x) is equal to ? How to answer this problem. Answered by Penny Nom. 





A volume in cubic yards 
20151112 

From James: The first formula for figuring cubic yards of concrete need is length in feet, times width in feet, times depth in actual inches, divided by 320. Such as, 150x 50 feet x 4inches divided by 320 = cubic yards. How and why does this formula work? Answered by Penny Nom. 





Factoring a trinomial 
20151102 

From Eric: 2v(squared) +11v +5 Answered by Penny Nom. 





Factor x^2 + y^2 
20150826 

From Jerome: Factor: x^2+y^2 Answered by Penny Nom. 





Factor 2(x+1)(x3)^23(x+1)^2(x3) 
20150813 

From Bella: The directions are the solve and factor the expression completely:
2(x+1)(x3)^23(x+1)^2(x3)
I was factoring out an (x+1) and and (x3) however the answer showing in my book is different and I can't figure out what I'm doing wrong please help Answered by Penny Nom. 





2^48  1 
20150613 

From Soham: The number 2^481 is divisible by two numbers between 60 and 70. The sum of
the two numbers is? Answered by Penny Nom. 





Prove that you cannot factor x squared + 5 
20150528 

From lily: the question is: prove that you cannot factor x squared + 5 Answered by Robert Dawson. 





The product of a 2digit number and a 3digit number 
20150206 

From Nathaniel: The product of a 2digit number and a 3digit number is about 50 000 what are the products Answered by Penny Nom. 





2x^22x+1=4x+1 
20150206 

From Caitlyn: 2x^22x+1=4x+1 Answered by Penny Nom. 





Factorise 15x + 15y 
20141120 

From Jordan: hi i saw a question in class today that i didn't understand and i didn't really understand what my teacher was going on about so how do you factorise 15x + 15y Answered by Robert Dawson and Penny Nom. 





Prime factorization in exponent form 
20141031 

From Emma: I need to find out how to make a prime factorization of 120 in exponential form. Answered by Penny Nom. 





A factoring problem 
20141005 

From Gina: 3x^2+6x+3 Answered by Penny Nom. 





Sieve of Eratosthenes 
20141003 

From Hope: using Sieve of Eratosthenes to determine for in instance prime numbers between 1 to 200, to what nth number should i stop?, 4th, which is 11 or what? Answered by Robert Dawson. 





Factorials 
20140606 

From penny: What is factorial? For eg. Like 2!, 3! 4! Etc. Answered by Penny Nom. 





Reducing the size of a poster by a scale factor of 1/3 
20140401 

From deeshon: eric is making a smaller copy of a poster that measures 20.4 cm wide by 34.2 cm long.he reduces the original by a scale factor of 1/3.what are the dimensions of the copy Answered by Penny Nom. 





2 rectangular prisms are similar by a scale of 0.75 
20140316 

From gina: 2 rectangular prisms are similar by a scale of 0.75. The volume of the smaller prism is 27cm3 (cubed). How many cubic centimeters is the volume of the larger prism? Answered by Penny Nom. 





Prime factorization 
20140206 

From Kadeejah: Write the prime factorization of 37 in exponential form Answered by Penny Nom. 





4x^37x^22x 
20140110 

From Alvi: 4x^37x^22x Answered by Penny Nom. 





Can 100r^281z^2 be factored? 
20131208 

From Rosa: Can 100r^281z^2 be factored? Answered by Penny Nom. 





Factor 
20131201 

From Rosa: How do you factor 9x^2  12y^2? Answered by Penny Nom. 





Factor strings 
20131014 

From Jane: What's a factor string? I'm confusey in the head. Answered by Penny Nom. 





a cubeb cubea+b= ? 
20130616 

From saryu: a cubeb cubea+b= ?
find the answer Answered by Penny Nom. 





Factor x^6  64 
20130125 

From Taylor: Hi, I am having trouble factoring x^664. Could you help me? Answered by Penny Nom. 





The zeros of a fourth degree polynomial 
20130123 

From Dakota: My problem has multiple steps and I have done everything but the last one. 8The original problem is f(x)=x^45x^3+7x^2+3x10 and I have to find the zeros of the equation. I used synthetic substitution like my teacher taught us to get the equation of x^33x^2+x+5=0 but now I don't know how to get the zeros of that equation, or solve it. Answered by Penny Nom. 





Difference of squares 
20121119 

From Qelibar: Please factorise x^2y^2  4 Answered by Penny Nom. 





Factor (6a^25a+1)(8a^26a+1)(12a^27a+1) 
20121116 

From bailey: Factorise f(a)=(6a^25a+1)(8a^26a+1)(12a^27a+1)
thus find [f(a)]^1/2 Answered by Penny Nom. 





Factoring 
20120910 

From saravanan: Dear Sir ,
I felt difficulty solving the following problem . So please help me .
a+b+c=7
ab+bc+cd= 20
what is a^2+b^2+c^2 ? Answered by Lorraine Dame and Robert Dawson. 





Factoring 
20120426 

From Amanda: y=x^29x Answered by Penny Nom. 





2x^2+5x+2 
20120423 

From eddie: 2x^2+5x+2 Answered by Penny Nom. 





What is the prime factor form of 7/5? 
20120417 

From David: What is the prime factor form of 7/5 Answered by Robert Dawson. 





A number puzzle 
20120407 

From Kenya: my number is less than 25
my number of tiles will make only one rectangle
my number is odd
my number is a factor of 36 Answered by Penny Nom. 





A cubic inequality 
20120325 

From Victoria: The flight path of a bumblebee above the ground can be modelled by the function f(x)= 2x^3 17x^2+ 11x + 130. Where x is the time in seconds and f(x) represents the height in inches above the ground. The entrance to the bee's hive is located 100 inches above the ground. Determine when the bumblebee's height is greater than 100 inches. The bee's height was monitored from 0 to 25 seconds inclusive. (over the domain 0 Answered by Penny Nom. 





Factoring a quadratic 
20120313 

From Makell: X^2 + 32x + 220 = 0 Answered by Penny Nom. 





Simplify the expression 
20120212 

From Christy: Hi guys, ok so I'm having problems with solving this equation since it's been so long I've done precal.
I have to find critical points so I have to find the derivative first. This is what I've done so far
s(t)= (t6)^4 * (t+1)^2
t'= 4(t6)^3*(1)*(t+1)^2+ 2(t+1)(1)*(t6)^4
so this is where I got stuck, which is the algebra part. How can I simplify this to get the answer to figure out the critical points. Answered by Penny Nom. 





factor 6x219x+3 
20111210 

From pedro: factor 6x219x+3 Answered by Penny Nom. 





Reducing by a scale factor of 1/3 
20111121 

From Sandra: A rectangle with the dimensions of 6.3 cm and 5.8 cm is reduced by a scale factor of 1/3. What are the dimensions of the new image? Answered by Penny Nom. 





Factor 
20111030 

From Dawn: x^2 6x+94y Answered by Penny Nom. 





Expanding the size of a table 
20111016 

From Ericka: You are working as a carpenter in an industrial Shop. A customer came to you and inquired about the size of the table which would be fitted in her room. She informed you that she had already a 1.5 x 1m table in her room but she wanted to maximize the space by adding the same amount to is length and width. She is planning to occupy a 3 square meter place on her room for her to work comfortably. She is requesting you a written recommendation before she asked to make a table. What amount should be added to both sides to maximize a 3 square meter area? Answered by Penny Nom. 





One factor array 
20110916 

From Hana: hi my brother a 5th grade have a question. this is what it say "i have only one factor array, and i am between two numbers 12 and 16. what number am i?" Answered by Penny Nom. 





A scale of 1:160 
20110502 

From Dave: a 4 foot by 8 foot sheet of plywood is how many acres in a scale (1:160) Answered by Penny Nom. 





(3x+4y)^2  (2xy)^2 
20110316 

From Taiwo: pls could some one help me with this question? thanks as lot
factorize:
(3x+4y)^2  (2xy)^2 Answered by Penny Nom. 





Factor 10x^2+17x6 
20110303 

From Jeff: Factor 10x^2+17x6 with steps and explanation. Answered by Penny Nom. 





(11/2)(22/3)(33/4)...(1515/16)=n!/16 
20110215 

From Fiona: Could you help me find the value of n: (11/2)(22/3)(33/4)...(1515/16)=n!/16 Answered by Penny Nom. 





Factoring with fractions 
20110215 

From Megan: Hi there,
I'm working on factoring polynomials but this question has me quite puzzled.. im a college student in my first year.
(x^2a^2/xy)(xy/x+a) Answered by Penny Nom. 





Scale factor 
20110125 

From Mackenzie: hi my problem is:
a man that is 6 feet tall in real life and only .5 inches in a =
photograph. what is the scale factor and scale of the photograph?
another:
a girl in the same photograph is 4.8 feet tall. How tall is she in the =
picture?= Answered by Chris Fisher. 





A scale drawing 
20101117 

From chandler: A parking lot 200 meters wide; 1 centimeter:25 meters, find the length on the scale drawing and the scale factor Answered by Penny Nom. 





A scale factor 
20101017 

From david: We have to rectangles with measurements and we need to find the scale factor. The rectangles are W=6 L=4 for first and second is W=4 and L=3.
thanks for your help Answered by Penny Nom. 





Rectangular arrays 
20100929 

From Kim: My 4th grader has started working on rectangular array that shows 2 factors of a number.
The problem reads on centimeter grid paper draw as many arrays as you can for each of the #'s 2,3,4, 5,6,7,,11,12,15 and 16. That would be great except I have no idea what they are talking about and I cannot offer any help to my daughter. Answered by Penny Nom. 





Factoring cubics and quartics 
20100929 

From Tori: How do you factor these types of questions:
* x^3  4x^2  x + 4
*2x^3  3x^2  4x  6
*x^4  15x^2  16 Answered by Robert Dawson. 





A scale model of a city 
20100518 

From Briana: Well I have to create a three dimensional city for a geometry project and it requires us to use precise scal factor and well we want to build a medium sized city but our teacher said that If we make or buildings to high our houses would look like super small compared to the tall building were trying to figure out if we were to build a medium sized city what scale factor should we use to make the houses big enough to see and design? Answered by Walter Whiteley and Tyler Wood. 





A quartic equation 
20100518 

From Austin: Z^410z^2=9 Answered by Penny Nom. 





Adding five positive integers that have a product of 48 
20100427 

From Lorraine: What is the smallest possible sum that can be obtained by adding five positive integers that have a product of 48. Answered by Chris Fisher. 





Factorials 
20100323 

From Leah: When should you use factorials? Answered by Robert Dawson. 





Factors and zeros of a polynoial 
20100317 

From Susan: find a polynomial function of degree three with 3 as a zero of multiplicity 2 and 4 as a zero of multiplicity 1. Answered by Tyler Wood. 





Scale factor 
20100202 

From Darlene: A towers actual height is 300m. An architect makes a scale drawing using a scale factor of 0.0001
A) how tall is the tower in the drawing?
B) if the drawing was 4cm high, what would the scale factor be? Answered by Penny Nom. 





(x+3) is a factor of 2x^33x^2+px+30 
20100109 

From Ruby: (x+3) is a factor of 2x^33x^2+px+30.
Determine the value of p Answered by Penny Nom. 





Factoring 
20100108 

From jim: i am having trouble with grade 12 factoring in general, i just do not understand it, please help! here is and example of a question:
12ac+28bc3ad7bd and it gets tougher from there like 7a(squared)14ab+7b(squared) any help is greatly appreciated Answered by Stephen La Rocque. 





The tens digit of 0! + 1! + 2! + 3! + ... + 2000! 
20091221 

From Alicia: What is the tens digit of 0! + 1! + 2! + 3! + ... + 2000!? Answered by Robert Dawson and Penny Nom. 





Factoring 
20091119 

From danyelle: 81x^2+36x+4
factoring i dont understand it at all Answered by Robert Dawson. 





Factors 
20091030 

From brenden: The numbers 3,5,7 are factors of n. Find four other factors of n besides 1 Answered by Penny Nom. 





An array 
20091028 

From felicia: what factors are shown in the array below?
**
**
**
**
**
** Answered by Penny Nom. 





Constructing a scale model 
20090927 

From Colleen: What is the formula i need to use to find out how to state a reasonable scale in the question below;
Suppose you were constructing a model that must sit on a piece of cardboard that is 22cm by 28cm. STATE THE REASONABLE SCALE that you can use to build a model to represent the following items. Determine the dimensions of the model.
a) a rectangular prism with a length of 5m and a width of 2m? Answered by Penny Nom. 





What is my number? 
20090918 

From Hanna: What is my number?
My number is a perfect square.
The only number in its prime factorization is 2.
My number is a factor of 32.
The sum of its digits is odd. Answered by Penny Nom. 





Exponential form 
20090831 

From cecil: what is the exponent form 564000? Answered by Stephen La Rocque and Harley Weston. 





Factoring 
20090823 

From Bj: Solve for x: 5x^2  35x = 0 Answered by Stephen La Rocque. 





HCF 
20090803 

From Nazrul: If (x+ a) be the H,C.F. of x^2+px+q and x^2+mx+n, prove that (pm)a=qn Answered by Stephen La Rocque. 





Dimensions 
20090729 

From Deborah: The blueprint for landscaping a yard has a scale of 1/2" to 1 foot. If the blueprint is a rectangle 18 inches by 22 inches, what are the dimensions of the yard? Answered by Robert Dawson. 





Highest Common Factor of Two Polynomials 
20090728 

From Nazrul: If x+a be the h.c.f. of x^2+px+q and x^2+mx+n, how can I prove that (pm)a=qn. Answered by Robert J. Dawson & Janice Cotcher. 





Using the Remainder Theorem to Find an Unknown Coefficient. 
20090706 

From Mukulu: What is the value of a if 2x2x6 ,3x28x+4 and ax310x4 have a common factor. Answered by Janice Cotcher. 





Factoring a quadratic 
20090616 

From Rebecca: solve the quadratic equation by factoring.
a) x(squared)+7x+10=0 Answered by Stephen La Rocque. 





The last non cero digit of a factorial 
20090612 

From Wilson: How can I find the last non cero digit from a factorial calculation of a big number.
For example 10! = 3628800, the last non cero digit is 8.
What is the last non cero digit of 10! ?? Answered by Robert Dawson. 





how do I factor 45  5x^2 
20090531 

From tracey: how do I factor 45  5x^2 Answered by Penny Nom. 





Factor 6x^2+19x+3 
20090526 

From michele: how do you factor this trinomial. 6x^2+19x+3 Answered by Penny Nom. 





Find out the length of a cup when its volume is halved 
20090525 

From Thomas: I'm having trouble with a question.
What kind of formula would i use to find out the length of a cup when its volume is halved? Answered by Stephen La Rocque. 





The dimensions of a larger cup 
20090523 

From Elizabeth: Hey
If i have a cup that holds a volume of 477mL and the bottom radius is 2.8cm and the top radius is 4.9cm and the height is 10cm. If i increase the volume by one and a half times what is the new measurements if the cup is directly proportional to the first one.
Thank you Answered by Stephen La Rocque and Penny Nom. 





Factor x squared(x3)+(x3) 
20090419 

From Victor: How do I factor x squared(x3)+(x3) ? Answered by Harley Weston. 





Find a polynomial function with the indicated zeros and satisfying the given conditions 
20090323 

From Kristen: Find a polynomial function with the indicated zeros and satisfying the given conditions. Simplofy your answer (no imaginary numbers or parentheses in the answer)
Zeros: 1+2i, 12i, 5 ; f(2)=1 Answered by Harley Weston. 





Surface area and scale factors 
20090221 

From tina: the surface area of a sphere is about 86 ft (2) find the surface area of a larger sphere that has a scale factor of 4 Answered by Penny Nom. 





The sequence 2n!  1 
20090201 

From Penny: I am trying to help my son with this problem. Find the first five terms of the sequence that can be written from the formula A= 2n !1. Answered by Penny Nom. 





How many students were there 
20090125 

From sooos: After a math lecture in university, the students go to the cafeteria. EACH ONE of them buys a cheese sandwich and a cup of tea. They ALL pay $18.49. How many students were they? Answered by Chris Fisher. 





Perimeters and scale factors 
20090124 

From dennis: I have this work that says how are the value of the ratios for the perimeters related to the scale factor? PLEASE HELP ME OUT Answered by Harley Weston. 





The tens digit of 0! + 1! + 2! + 3! + 4! .............+9999! + 10000! 
20090123 

From Kaylyn: determine the tens digit for the expression:
0! + 1! + 2! + 3! + 4! .............+9999! + 10000! Answered by Robert Dawson and Penny Nom. 





Factor x^2  y^2 
20090120 

From Shell: complete Factor: x^2y^2 Answered by Penny Nom. 





The factors of an integer 
20090106 

From Madison: what are the factors of 878 Answered by Robert Dawson. 





Do all square numbers have an odd number or factors? 
20081211 

From Amy: Do all square numbers have an odd number or factors? Answered by Victoria West. 





Factor 9x^2 + 6x + 4 
20081121 

From Jonah: how can i solve this by factoring: 9x^2 + 6x + 4 Answered by Harley Weston. 





Factoring 
20081119 

From Neji: How do you factor (yz) (y+z) (y^4+y^2z^2+z^4) and get (y+z)(y^2yz+z^2) (yz) (y^2+yz+z^2) as the answer? Answered by Harley Weston. 





Real and imaginary zeros 
20081112 

From David: Find all the real and imaginary zeros for each polynomial. Factor each polynomial. Leave factors with imaginary zeros in quadratic form.
h(x)= x^5 +2x^4  10x^3 20x^2 +9x + 18 Answered by Harley Weston. 





The prime factorization of one billion 
20081102 

From Alta: The prime factorization of 1000 is 2 cubed times 5 cubed. How do you write the prime factorization of one billion using exponents? Answered by Penny Nom. 





2x^3+x^22x1=0 
20081026 

From bobby: 2x^3+x^22x1=0 Answered by Penny Nom. 





Factor completely 
20081022 

From Monica: I have to factor the following two items completely, but I am lost. I've tried factoring by substitution and grouping but they don't seem to work:
1. 5(w3z) 10(w3z)=
2. ab21+a3b7= Answered by Penny Nom. 





Prime factorization 
20081019 

From nick: while im doing prime factorization for one number and it cant be divided 2,3 or five so what next? Answered by Penny Nom. 





a(a+1)  b(b+1) 
20080930 

From Shaun: I need to factor (ab) out of the following: a(a+1)  b(b+1). I know it is simple but I cannot remember how. Answered by Penny Nom. 





Number of factors 
20080918 

From Austin: I am stuck on finding what type of number has exactly two factors and
what type of number has an odd number of factors? I need some examples. Answered by Penny Nom. 





Simplifying Algebraic Expressions 
20080822 

From Jacky: x^2y^2+4x+4y Answered by Penny Nom. 





Factoring x^2 + 729 
20080819 

From peter: hello I,am having trouble factorising a polynomial into polynomial factors
with real coefficients please can you help the polynomial is x^2+729 Answered by Harley Weston. 





Product of TwoDigit Numbers 
20080731 

From pete: The number 4641 can be expressed as the product of two twodigit whole numbers. What is the sum of these two numbers? Answered by Janice Cotcher. 





Factoring a quadratic trinomial 
20080721 

From Jeff: c^2+4c+4
x^27x18 Answered by Penny Nom. 





Number of factors 
20080720 

From pete: how do you find the number of factors in a really big number without using a factoring program or listing the out? Answered by Penny Nom. 





n choose r equals n1 choose r plus n1 choose r  1 
20080714 

From fae: Prove that
( n ) = ( n – 1) + ( n  1 )
( r ) ( r ) (r1)
NOTE: the ( ) should be one for n taken r and so on. but there is no one big ( ) that will cater two lines Answered by Janice Cotcher. 





What is the largest perfect square factor of 1512? 
20080702 

From peter: What is the largest perfect square factor of 1512? Answered by Penny Nom. 





The square root of (18*n*34) 
20080701 

From Peter: What is the least possible positive integervalue of n such that square root(18*n*34) is an integer? Answered by Penny Nom. 





How many positive integer factors of 2^2*3^2*5 are multiples of 12? 
20080627 

From Peter: How many positive integer factors of 2^2*3^2*5 are multiples of 12 Answered by Janice Cotcher. 





4x^3  6x + 2 = 0 
20080528 

From paul: 4x^3  6x + 2 = 0 Answered by Janice Cotcher. 





Scale factor 
20080528 

From Riley: I have a math problem, and a big test coming up on Friday or Thursday (my teacher hasn't decided yet.) I need help understanding how
I would do this problem. Here it is: they wanted me to find the perimeter and area of a rectangle when they only give me the scale factor. I've
delt with scale factors before, but this is quite confusing. I have done the scale factor way by having a rectangle that maybe has a width of 10 and a
height of 20, and I needed to find what the scale factor would be for a rectangle with the width of 5 and a height of 10. I know that they scale factor
would be 2, right? But this just gives me the scale factor, and I have to FIND the perimeter and area. Hopefully you can get back to me tonight. Answered by Harley Weston. 





The area of a rectangle 
20080527 

From Becky: the area of a rectangular lot is represented by 6t^2+13t5. What are the length and the width of the rectangular lot? Answered by Harley Weston. 





Prime factors 
20080521 

From john: the first 5 prime numbers are 2,3,5,7,11. which is the smallest number that has these prime factors. Answered by Stephen La Rocque. 





The factor theorem 
20080506 

From Nomaan: factorise
x³2x²x+2
using factor theorem Answered by Penny Nom. 





Factor ac^2  a^3  a^2b + ab^2 + b^3  bc^2 
20080505 

From erson: factorize:
ac^2  a^3  a^2b + ab^2 + b^3  bc^2 Answered by Harley Weston. 





(9x^24)/(3x^25x+2) * (9x^4  6x^3 +4x^2)/(27x^4+8x) 
20080429 

From Jonathon: I don't remember how to solve an equation in the form of the following:
(9x^24)/(3x^25x+2) * (9x^4  6x^3 +4x^2)/(27x^4+8x) = Answered by Stephen La Rocque. 





The ratio of their perimeters to two regular hexagons 
20080429 

From td: Two regular hexagons have areas of 54 square root of 3 and 150 square root of 3, what is the ratio of their perimeters? Answered by Stephen La Rocque. 





Factor and solve s1^2  10s1  200 = 0 
20080429 

From KIM: please factor and solve s1^2  10s1  200 = 0 Answered by Stephen La Rocque and Penny Nom. 





The zeros of a cubic 
20080409 

From Ryan: what are all the zeros of f(x)= x^31/2x^2+1/3x1/6 Answered by Penny Nom. 





Factor 2x^3 + 3x^2  32x + 15 
20080402 

From sarah: I have a course review I'm working on and I'm not sure how I'm supposed to factor the following
2x^3 + 3x^2  32x + 15. Answered by Penny Nom. 





The number of positive integer factors 
20080402 

From lisa: If n is a positive integer such that 5n has 36 positive factors, and 3n has 40 positive factors:
How many positive factors can 15n have? How many values are possible for n? Answered by Penny Nom. 





(x3)/(xcube+6xsquare25x150) 
20080324 

From rafia: (x3)/(xcube+6xsquare25x150) Answered by Penny Nom. 





How would I factor 2x^3 + 11x^2  7x  6? 
20080322 

From Sean: How would I factor this polynomial?
2x^3 + 11x^2  7x  6 Answered by Stephen La Rocque. 





How would I graph: x  2 divided by x^2  4? 
20080319 

From Sean: How would I graph: x  2 divided by x^2  4 using a method in extreme values of
functions or completing the square
x  2/ x^24 Answered by Stephen La Rocque. 





Graph the equation P(x)= x^3 + x^2 12x 
20080318 

From Sean: I want to graph the equation : P(x)= x^3 + x^2 12x I was thinking that I would combine
the xvalues, but then I could not use the complete the square technique. Would I have to
just solve the second half of the equation and then graph x^3 seperately Answered by Penny Nom. 





A dilation project 
20080312 

From john: I am working on a dilation project.
How do I dilate an irregular octagon on a scale of 3.5 Answered by Stephen La Rocque. 





Factor x^65x^3+25 
20080311 

From jacob: how do you factor equations for algebra 2
x^65x^3+25 Answered by Harley Weston. 





The dimensions of a rectangle 
20080306 

From Julie: Find the dimensions of a rectangle with an area of 400. Width x ft.
Length (2x7)ft. Answered by Stephen La Rocque and Penny Nom. 





Two regular pentagons 
20080227 

From Shirley: Regular pentagon QRSTU has a side length of 12 centimeters and an area of
248 square centimeters. Regular pentagon VWXYZ has a perimeter of 140
centimeters.
I need to find its area. Answered by Stephen La Rocque. 





Factoring a trinomial 
20080220 

From Adrienne: a field an rea of (x^2+x6) square metres. State expressions for its length and width. Answered by Penny Nom. 





Growth factor and growth rate 
20080213 

From william: what is the difference between growth factor and growth rate? Answered by Stephen La Rocque and Harley Weston. 





Scale factors 
20080213 

From Dayne: My teacher doesn't now how to teach us scale factors and i have a problem to make it easier to understand. The problem is: A map of Levi's property is being made with a scale of 2 cm : 3 meters. What is the scale factor? Answered by Stephen La Rocque. 





5x squared  15x  200 
20080211 

From Catherine: I am having a problem solving this question:
5x squared  15x  200 Answered by Penny Nom. 





5x^2  45 
20080211 

From Tiana: factor:
5x^2  45 Answered by Stephen La Rocque. 





Sum of factorials 
20080126 

From Emily: What is the tens digit in the sum 7! + 8! + 9! ... + 2006! Answered by Stephen La Rocque. 





(303,000,000,000,303x3,300,000,033)/1,000,100,010,001 
20080113 

From Adrian: Give the result of the following computation as an integer.
(303,000,000,000,303x3,300,000,033)/1,000,100,010,001
N.B. No calculators allowed Answered by Penny Nom. 





Factoring x^2 + 25 
20080104 

From Geri: what does x squared plus twenty five factor out to? Answered by Penny Nom. 





A bronze statue is made in two sizes. 
20071217 

From Sara: Hello!
A bronze statue is made in two sizes.
The taller statue is 15 cm high and the shorter one is 9 cm high.
The taller statue weighs 3.75 kg. What is the weight of the shorter statue? Answered by Penny Nom. 





What length scale factor should he use? 
20071216 

From Lisa: Hi! Joe wants to enlarge a picture so that its area is doubled.
What length scale factor should he use? Answered by Penny Nom. 





8^2+64^2 
20071112 

From Daniel: I am having trouble factoring equations like 8^2+64^2, I just don't know
the correct steps to get the answer. Answered by Penny Nom. 





Prime factorization 
20071111 

From jeff: find the prime factorization and use exponential notation for 432 Answered by Penny Nom. 





13 year and 17 year locusts 
20071012 

From stefan: how many years pass between the years when both 13 year and 17 year locusts are out at the same time? Answered by Penny Nom. 





What is a friendly Factor? 
20071012 

From Christine: Hi mi niece and I are trying to figure out what friendly factors are. An example of one of the questions: Use friendly factors to multiply the following. 8x25=.
Can you please help? thank you Answered by Penny Nom. 





Simplifying rational expressions 
20071009 

From Bama: x(x2)+1 divided by x^23x+2 Answered by Stephen La Rocque. 





Factoring quadratics 
20071009 

From Abbie: I have two problems same topic. I belive they cannot be factored but i want to make sure.
x^{2}+6x40
x^{2}20x+99 Answered by Penny Nom. 





Finding the last nonzero digits of large factorials 
20071004 

From Mukesh: i have to find last five non zero digits of integer which can be very large (
upto 10^12) . i can find last non zero digit of of any factorial. Now my problem is that
i have to find last five non zero digit of factorial and also i want to general method for
last K non zero digits of factorial n. For example 10!=3628800 so last non zero digit is 8 ,last two
non zero digit is 88 .....and last five non zero digit is 36288. Answered by Victoria West. 





8x^3 + 4x 3 
20071002 

From Indrajit: 8x^3 + 4x 3 Answered by Stephen La Rocque. 





What are the factors of 111? 
20070913 

From Miska: What are the factors of 111? Answered by Penny Nom. 





The factors of 35 
20070911 

From johh: wats the factors for 35 Answered by Penny Nom. 





Find All 24 Factors Of 360 
20070908 

From Jennifer: Find All 24 Factors Of 360 Answered by Penny Nom. 





Prime factors in exponential form 
20070906 

From Michelle: how would you write this: factor 48 as a product of primes written in exponential form Answered by Stephen La Rocque. 





Factoring a quadratic 
20070904 

From Arlene: Question from arlene, a student:
x^+2x24=0 Answered by Stephen la Rocque. 





Factor completely 2x^23x5 
20070828 

From melissa: how do you factor this completely:
2x^23x5 Answered by Stephen La Rocque and Penny Nom. 





Common factors 
20070819 

From John: I have problem factorising 2p^3  34p. Please advise me. Answered by Leeanne Boehm, Steve La Rocque and Penny Nom. 





10r^2  35r = 0 
20070813 

From Aranxa: how do u solve this equation by factoring:
10r^2  35r = 0 Answered by Penny Nom. 





Can you solve this by factoring? 10r^2  35r = 10 
20070812 

From Aranxa: how do u solve this equation by factoring:
10r^2  35r = 10 Answered by Stephen La Rocque. 





Factorial fraction 
20070803 

From Sekhoane: Expand completely: (N2)!/N!(9N1)! Answered by Stephen La Rocque. 





A model for a building 
20070717 

From Carl: A model for a building is 50 centimeters long, 38 centimeters wide, and 225 centimeters tall
on model 1 centimeter represents 2.5 meters.
I need to find the volume of the actual building in cubic meters,and the surface area of the building including
ceilings and floors. round to the nearest tenth of a square meter. Answered by Harley Weston. 





An odd number with 12 factors 
20070627 

From Wilson: Do you know of any odd number that has 12 factors? Reply back today.
Because I have hand in a project tomorrow. Answered by Stephen La Rocque and Harley Weston. 





Factor X^6  64 
20070620 

From Krystal: How do I Factor X^6  64 into linear factors? Answered by Penny Nom. 





Simplifying a quartic rational expression using long division 
20070614 

From Megan: x+2/12x^4+17x^3+0x^2+8x40= Answered by Stephen La Rocque and Penny Nom. 





Converting dollars to gallons 
20070612 

From Cynthia: How do I solve this problem?
If a family uses .20 per 100 gallon of water. How many gallons would
$10.00 cost, divided amoung 3 people?
Thanks, Cynthia Answered by Stephen La Rocque. 





Finding the area of a lot without knowing the angles 
20070605 

From Cristin: I have a landlocked piece of land. I need to know the square
footage in order to determine the acreage. My deed only gives the lengths of its five sides. Answered by Stephen La Rocque. 





Factor Completely 
20070529 

From Ema: Question 1:
Factor completely.
3x(x – 4) + 5(x – 4)
Question 2:
Factor completely.
x^2 + 2x + 3 Answered by Penny Nom. 





A scale factor 
20070528 

From Chandler: I am rather confused about finding the area of a triangle they give me the area of the larger triangle it is 25 units but I can't figure out how to find the area of the smaller triangle the scale is 3:5 please help me ASAP. Thanks so much I really appreciate it oh the triangles are similar Answered by Stephen La Rocque and Penny Nom. 





Factoring a trinomial in two variables 
20070523 

From Ema: How do you factor this completely. x^5y^33x^4y^228x^3y Answered by Stephen La Rocque. 





Combinations 
20070509 

From Michael: Show that 5 X C(n,5) = n X C(n1,4) Answered by Stephen La Rocque. 





Probability of getting an A 
20070509 

From Christine: In a class of 15 people, exactly 3 got an A. If 2
people are randomly chosen from this class, what is the probability that
at least one of these 2 got an A? Answered by Paul Betts. 





Factor by grouping 
20070416 

From Vincent: How do you factor
the ( ) are exponents
4b4b(3)+ a(2)b  4a  ab(4)
I still don't understand if there is no a in 4b4b Answered by Penny Nom. 





Factoring by grouping 
20070413 

From vincent: How would you factor
the number in ( ) are exponents
2b(3)+3a(3)+3ab(2)+2a(2)b =
and
4b4b(3)+a(2)b  4a  ab(4) = Answered by Haley Ess. 





Reducing the over all size of a irregular pentagon 
20070411 

From Gilbert: I'm having trouble figuring out how to reduce the over all size of a irregular pentagon.
The pentagon I'm trying to reduce has 2 right angles adjacent to each other.
Basically the shape of a house. I have width, length of the legs and the height of the peak.
But cannot figure out how to get the size of a reduced version that keeps the same proportion
and angles.
Thanks
Gilbert Answered by Penny Nom. 





Factoring a trinomial 
20070327 

From Kim: Hi, could you please help me solve this.
3x(squared) +20x  7 Answered by Leeanne Boehm. 





n1/(n+1)! + n+1/n! 
20070318 

From Cody: How do you go about simplifying something like this;
n1/(n+1)! + n+1/n!? Answered by Steve La Rocque and Claude Tardif. 





(x+2) is a factor of x^3+bx^214x+24. Find the value of b? 
20070311 

From victoria: hi my names victoria and i have been stuck on this question for ages can you please help me! (x+2) is a factor of x^3+bx^214x+24. Find the value of b? Answered by Penny Nom. 





If the product of A,B,C is 15834, what is A+B+C? 
20070310 

From rachel: if the product of A,B,C is 15834, what is A+B+C? Answered by Penny Nom. 





What exactly is a factor of a number? 
20070304 

From ASHLEY: What exactly is a factor of a number? Answered by Penny Nom. 





The factor theorem 
20070304 

From Sophia: hi this is sophia, 10th grade from the philippines. im really having a hard time in factor theorem im just asking if you could help me solve these problems because i really dont have an idea on how to do solve these.. please
find the values of A and B so that (x+3) (x2) are both factors of x^3+Ax^2+Bx12
and
find the values of A, B, and C so that (x3) (x+1)and (x2) factors of P(x)=x^4+Ax^3+Bx^2+Cx+12
please help me.. i really do not understand these problems Answered by Penny Nom. 





Factoring polynomials 
20070214 

From Joe: I am in the eighth grade, and we are learning the equivalent of Algebra 2. I have no ides how to factor (x2)(x^21)6x6 You help is most aprreciated. Thank you! Joe Answered by Stephen La Rocque. 





Greatest common factor 
20070126 

From Alexis: What is the greatest common factor of 52,and 100? Answered by Penny Nom. 





Factoring m^49^n 
20061207 

From Josh: I can not figure out how to completely factor m^49^n. Answered by Penny Nom. 





Factors 
20061122 

From Jacqueline: Why do the numbers 16,36,48,60,64,90 and 100 have an odd number of factors? Answered by Stephen La Rocque and Penny Nom. 





How do I factor 10x^2 + 17x + 6? 
20061121 

From Sheldon: How do I factor 10x^2 + 17x + 6? Answered by Penny Nom. 





Scale factors and ratios 
20061119 

From Maggie: I have a BIG math test coming up, and it's about scale factors and ratios, but i don't understand them at all. How can you tell the difference between scale factors and ratios? and How are they used in the everyday world? Answered by Penny Nom. 





When kx^2+3x+1 divided by (x2) the remainder is 3 
20061109 

From Brianna: For the dividend, find the value of k if the remainder is 3. (kx^2+3x+1) divided by (x2) Answered by Penny Nom. 





The sum of two numbers is 30 
20061103 

From GG: The sum of two numbers is 30 and the product of the same two numbers is 221. Find the two numbers. Answered by Stephen La Rocque. 





An odd number of factors 
20061028 

From Anthony: What is the common name used for numbers that have an odd number of factors? This answer should be a two word answer only. Answered by Stephen La Rocque. 





The greatest common factor 
20061017 

From Myrna: What is the greatest common factor of 49,164 and 80,860 Answered by Stephen La Rocque. 





X^1/3X^1/9=60 
20060926 

From Harini: I need the answer for
The value of X in X^1/3X^1/9=60. Answered by Penny Nom. 





How do i factor x^3  6x^2 + 8x 
20060910 

From Lauren:
how do i factor
x^{3}  6x^{2} + 8x
Answered by Stephen La Rocque. 





How many total worker are in the factory? 
20060826 

From Sherine: One quarter of the workers at the factory are clerical, one fifth are technical, half are are administrative,and the remaining 25 are managerial.
How many total worker are in the factory? Answered by Penny Nom. 





Find the divisors 
20060821 

From Minh: Using combination or permutation or both, find the
a. Divisors
b.even divisors
of 2160 Answered by Stephen La Rocque and Penny Nom. 





When 391758 and 394915 are divided by a certain three digit number, ... 
20060726 

From Nick: When 391758 and 394915 are divided by a certain three digit number, the three digit reminder is the same in each case. Find the divisor. Answered by Chris Fisher and Steve La Rocque. 





The greatest common factor of two numbers 
20060716 

From Fadwa: What is the greatest common factor(GCF) of the following algebraic expressions? 1680 and 6048
Answered by Stephen La Rocque. 





Factor 81x^4  72x^2 + 16 
20060619 

From Jesse:
how would i factor this?
81x^{4 } 72x^{2} + 16
Answered by Penny. 





How many numbers are relatively prime with 250? 
20060419 

From David: How many positive integers less than or equal to 250 are relatively prime with 250? Answered by Stephen La Rocque. 





How to find the odds for a lottery jackpot 
20060412 

From Harvey: Is it best to use factorials to calculate the odds of winning a lottery, such as the MegaMillions that is popular in the US, or is there a better way? Answered by Stephen La Rocque. 





x^2+2x3 is a factor f(x)=x^4+2x^37x^2+ax+b 
20060406 

From Maha: Given that x^{2}+2x3 is a factor f(x)=x^{4}+2x^{3}7x^{2}+ax+b, find a and b and hence factor f(x) completely. Answered by Penny Nom. 





A scale factor 
20060325 

From Jackie: I need a formula or step by step help to show my child how to find missing dimensions for example: The scale factor for a model is 10 inches = ________ feet
Model 39.7 in
Actual 11.9 ft Answered by Penny. 





GCD 
20060320 

From Jana: How can i prove:
if gcd(a,b)=1 then gcd(a+b,ab)=1 Answered by Penny Nom. 





f(x) is a polynomial of degree 3. 
20060313 

From Meadow: f(x) is a polynomial of degree 3. It leaves a remainder of 10 and 4 when divided by
x + 1 and x  2 respectively. Given also that f(1) = f(2) = 0, find the remainder when
f(x) is divided by x  3. Answered by Penny Nom. 





Factor 
20060308 

From Brad: Factor:
x^{3} + 64m^{3} and 125p^{3}  q^{6} Answered by Penny Nom. 





Factors of a cubic 
20060308 

From Skye: Show that (x+2) is a factor of f(x) where:
f(x) = px^{3} + (4p+2)x^{2} + (5p+4)x + 2p
Find the range of values for which the equation f(x) = 0 has 3 distinct real roots Answered by Penny Nom. 





The quadratic formula 
20060303 

From Miriam: Please show work and indicate "answer", using the quadratic formula 
(x+2) (2x+3) = 6 Answered by penny Nom. 





6y^10 + 19y^5 + 14 
20060302 

From Bahija: Factor 6y^{10} + 19y^{5 }+ 14 Answered by Penny Nom. 





X^2 + 4X + 6 is a factor of X^4 + rX^2 + s 
20060211 

From Katie: If X^{2} + 4X + 6 is a factor of X^{4} + rX^{2} + s, then find the value of r+s? Answered by Steve La Rocque and Penny Nom. 





How many divisors does the number 138600 have? 
20060208 

From Joe: How many divisors does the number 138600 have? Answered by Steve La Rocque and Penny Nom. 





Highest common factor 
20060206 

From Sajid:
1.A rectangular field has dimensions 156 m and 84 m. It is to be fenced with wire netting supported by stakes, equally spaced, a stake being placed at each corner of the field. What is the greatest possible distance between any two stakes, given that it should be more than 2 m and less than 8 m?
2. What is the length of the side of the largest square tile which can be used to cover a floor 525 cm long by 275 cm wide without leaving a gap?
3. Find the greatest number which will divide 140 and 249 to leave remainders 8 and 18 respectively?
4. Find the greatest number which will divide 304 and 298 so as to leave remainder 4 in each case.
Answered by Penny Nom. 





Prove that p^n >= (p!)/(pn)! 
20060202 

From Rhydian:
PROVE:
p^{n} >= (p!)/(pn)!
Answered by Penny Nom. 





Four people are in a race 
20060126 

From Tammy: If 4 people are in a race, how many different placements, i.e., 1st, 2nd, 3rd, 4th, can there be and what is the equation? Answered by Penny Nom. 





5x^2  27x  18 
20060113 

From Katy: How would you factor 5x^{2}  27x  18? Answered by Penny Nom. 





GCF, LCM, primes and the ladder method 
20060107 

From Linda: How would I teach both finding the GCF and LCM with prime factors...I recall the ladder method vaguely.??? Answered by Penny Nom. 





3x^4  81 
20060102 

From Julio: How can I factor the following?:
3x^{4}  81 Answered by Penny Nom. 





LCM 
20051212 

From Alex: what is the LCM of 210 and 54 and the LCM of 42 and 126 Answered by Penny Nom. 





Numbers with exactly 5 divisors 
20051123 

From Mary Lou: Show the 10 numbers with exactly 5 divisors. Answered by Penny Nom. 





Factoring quartics 
20051113 

From Kyle: How do I factor y^{4} + y^{2} +1?? I think the answer is (y^{2} + y + 1)(y^{2}  y + 1), but I'm not sure how to get that... Answered by Chris Fisher. 





Factoring 
20051030 

From A student: Factor 18x^{3} y^{3} + 12xy^{2} Answered by Penny Nom. 





Divisibility by each of the first ten counting numbers 
20051017 

From Simon: determine smallest positive integer that is divisible by each of the first ten counting numbers Answered by Penny Nom. 





The remainder theorem 
20051007 

From Ron: If f(x) is divided by (x3), the remainder is 5, and if it is divided by (x+1), the remainder is 3. Find the remainder when f(x)is divided by (x3)(x+1). Answered by Chris Fisher. 





An odd number of factors 
20051006 

From Ramneek: What is the common name used for numbers that have an odd number of factors? Answered by Claude Tardif. 





How do you solve 3x^2 + x  2 = 0 
20050915 

From Lizzy: How do you solve 3x2 + x  2 = 0 Answered by Penny Nom. 





A quadratic 
20050906 

From Ginger: I took a pre alg test today. There was a question on it that I am not sure and is bothering me. Can you tell me the answer?
x square + 13 + 14
Factor this Answered by Penny Nom. 





Which number is greater? 
20050818 

From Dante: Which number is greater: 888....88 X 333...33 or 444.......44 x 666........67 (each of the numbers has 1989 digits)? Answered by Claude Tardif. 





An algebraic remainder 
20050622 

From Raymond: Given that 4x^{3}  kx is divisible by 2x+1, find the remainder when the expression is divided by 4  x^{2}. Answered by Penny Nom. 





Factoring 
20050520 

From Abraham: Can you please explain to me how to factor completely the following problem:
(sqrt(x+1))((x^{2}+2x+1)^{( 7/4)}). Answered by Penny Nom. 





16x^2+20x12x15 
20050503 

From Tanya: how they got (4x+5)(4x5) from
16x^{2}+20x12x15=4x(4x+5)3(4x+5)=(4x+5)(4x5) Answered by Penny Nom. 





A 3digit product 
20050225 

From A student: I have an odd 3 digit product. My factors are a 1 digit number and either a 2 or 3 digit number. My factors are odd, but neither is 1. Find my factors and my product. Answered by Penny Nom. 





Factoring a cubic 
20050220 

From Abraham: How would you factor completely,
x^{3}x^{2}+5x5? Answered by Claude Tardif. 





Numbers that John likes 
20050116 

From Garrett: John likes 400 but not 300; he likes 100 but not 99; he likes 3600 but not 3700. Which does he like?
900
1000
1100
1200 Answered by Penny Nom. 





252 x ? is a cube 
20041222 

From Andrea: What is the smallest positive interger by which 252 can be multipled so the result is a perfect cubed? Answered by Penny Nom. 





"a" cubed minus "b" cubed 
20041202 

From Denise: "a"cubed minus "b"cubed equal (ab) times
("a"squared plus "ab" plus "b"squared)?
I know this is a formula, but why is it true? Answered by Penny. 





Solving quadratics 
20041120 

From Aaron: Can you solve the following equation (quote the value of x,y and t to 3 sig figs)
((i have changed figures so that i can work through my own example))
x^{2} + x  6 = 0
5y^{2} +19y = 3
10cos2 t + 3cos t = 4 Answered by Penny Nom. 





An ODE 
20041110 

From David: I have a question that i really cant do, it is as follows:
The ODE dy/dx + 0.5y = 0.5e^(1.5x) ; y(5) = 2
Solve the ODE subject to the given condition using exact methods and evaluate the solution y for x = 5 x=5.2 x=5.4 x=5.6 x=5.8 x=6 Answered by Harley Weston. 





Factoring 
20041109 

From Rise: Q1: a^{2} + 5a + 6
I didn't really understand the purpose of the teacher's steps, but was able to get my daughter to find factors of 6 and then add them together to find which resulted in the sum of 5.
Unfortunately, this problemsolving technique did not help us to solve for the more complex problems as follows:
Q2: 9a^{3}  24a^{2} + 12a Answered by Penny Nom. 





Multiplying two algebraic fractions 
20041031 

From A parent: Multiply:
x+2 x²4
 x 
x2 x²+x2 Answered by Harley Weston. 





GCD and LCM 
20041031 

From Cartalina: how do you calculate the "positive difference between the GCF and LCM of two numbers"? Answered by Penny Nom. 





Crossword math puzzle 
20040914 

From Joyce and Tiffany: The puzzle name was real number vocabulary and the question is (a number that divides evenly into another what is it?). (Space in between ticmarks on a number line). Answered by Harley Weston. 





GCD (a + b , a^2  ab + b^2) 
20040827 

From Carol: Let a and b integer and relatively prime. Proof that:
GCD (a + b , a^2  ab + b^2) = 1 or 3 Answered by Penny Nom. 





The integrating factor method 
20040805 

From A student: Whilst using the integrating factor method, I am required to integrate a function multipled by another function.
say f(t) = exp(kt) and some other function g(t); where exp = exponential and k is some constant.
Integral f(t)*g(t) dt or
Integral exp(kt)*g(t) dt
What would the result of this integral be? I have never met an integral like this before. Would it simply be exp(kt)*g(t)/k?
More specifically, the problem and my attempted answer is in PDF format:
In my attempted solution, I am unsure about the last two lines I have written out, as it relates to integrating a function multipled by another function. Answered by Harley Weston. 





an integer with three factors 
20040803 

From A student: What is the probability that a randomly chosen 3 digit number has exactly 3 factors Answered by Penny Nom. 





sin^2x5sinx3=0 
20040802 

From Kerri: hey my name is kerri i'm a college students and i was wondering if you could help in with this problems
sin^2x5sinx3=0 Answered by Penny Nom. 





Factoring 
20040728 

From Nicole: Can 4x2 + 19x + 12 be factored? i have tried but i cannot figure it out. Is there a way to find out if it cannot be factored before i try to work out the problem? Answered by Penny Nom. 





x^2 = x + 2 
20040726 

From A parent: x2 = x+2
My daughter came home with this equation today and although I know the answer is x=2, i have no way of proving it by showing any working out. Answered by Penny Nom. 





Factoring 
20040719 

From A student: Factor completely:
3x3  24y3
54x6 + 16y3
16xy  4x  4y  1
0.09x2  0.16y2 Answered by Penny Nom. 





Solving some quadratic equations 
20040715 

From A student: Could you please solve the following for x
x^{2}+6=5x
x^{2}+16=8x
2x+21=3x^{2} Answered by Penny Nom. 





Factoring integers 
20040702 

From A student: After looking at all the info I could get about NFS, I still have some questions that are unsolved:
First of all: If someone found an algorithm that has a worst case running time of N*Log(N) to factor an integer n into his divisors, would it be quicker or slower then the number field sieve algorithm?
secondly, what exactly is the time complexity of the Number Field Sieve algorithm, if I would factor an integer n? Answered by Claude Tardif. 





112! 
20040528 

From Beatriz: 1) A bus driver collects identical sets of 5 coins from each passenger. If the totoal colledted was $21.83, how many pennies did the driver get??
2) How many terminal zero in the base 10 expression of 112! (factional) N! means N(N1)(N2) .....(2) (1). Answered by Penny Nom. 





Factoring 
20040427 

From Bipin: FACTORISE:
a to the power of 6 + b to the power of 6 Answered by Penny Nom. 





Some factoring problems 
20040415 

From KJ: Factor these:
x^{3}+125 > (x+5)^{3}
8x^{3}27 > (?)
x^{2}+36 > (x+6)^{2}
x^{4}5x^{2}+4 > (?) Answered by Penny Nom. 





n! > n^2 
20040330 

From Jose: How can you prove by mathematical induction that:
n! > n2. Answered by Penny Nom. 





Factoring x^2 + 5x + 4 
20040314 

From Keenan: how do I factor x^+5X+4? Answered by Penny Nom. 





The factor theorem 
20040308 

From LisaMarie:
Hi, I have a career link question from gr.12 advanced functions
and intro. calculus. The equations is:
R(t) = 5(t^{4}  4t^{3} +
19/4 t^{2}  3/2 t)
The question is to apply the factor theorem
and quadratic formula to determine the times it crosses the t axis. The
only method i know of for using the factor theorem is when the last number
does not have a variable beside it so i'm not sure how you would even
use the factor theorem for this? We haven't dealt with any that have 0 as
the last number with no variable so i'm a little confused! please help!
Thank you
Answered by Penny Nom. 





Factoring expressions 
20040103 

From A student:
I'm having trouble factoring expressions that aren't monic. I can do things like
x29x+8, but problems like 12x2+5x3 have me stumped.
I also have a question about factoring out common factors. In a problem like
x218x+81, wouldn't you divide by 9? But what happens to the x2, is it x2/9? Answered by Penny Nom. 





Multiplier and multiplicand 
20031217 

From Karen: The K5 curriculum states that at a grade 5 level students should "understand and use the terms multiplier, multiplicand" The curriculum defines 'multiplicand' as " a number being multiplied by another number. A factor." There is no definition given for 'multiplier'
Question: Define these words are they just other words for 'factors'. If so, how important is it that students use these terms? It would seem like 'factors' would be the better choice of words to use. If multiplcand refers to eg. the first factor in the equation and the 'multiplier' the seond term, (if in fact it does) is this not confusing for students when we teach them that multiplication is commutative? Answered by Penny Nom. 





Factoring in 
20031216 

From Priscilla: How can you use solving by factoring in real life applications? Answered by Harley Weston. 





What is a number that has exactly 13 factors? 
20031109 

From Mary: What is a number that has exactly 13 factors? Answered by Penny Nom. 





Greatest Common Factor 
20031108 

From Beth: How do you use the Greatest Common Factor in addtion and subtraction of fraction? Answered by Penny Nom. 





Which one has the most factors? 
20031031 

From Kristi: Of all the whole numbers less than or equal to 5000, which one has the most factors? Answered by Claude Tardif. 





Pairs of prime numbers 
20031013 

From Nikolas: Use pairs of prime numbers to find all the numbers less than 50 that have only two prime factors. Make an organized list. Answered by Penny Nom. 





Relatively prime 
20030927 

From James: what is the definition a relative prime numbers? Answered by Penny Nom. 





Making a square 
20030907 

From A student: if I am given any number (say 80 for example), how may I determine the smallest whole number integer which when multipled by it will yield a square number ? In other words if I express this as: 80Ý*ÝnÝ=ÝsquareÝnumber, what is the least value of n which will yield a square. Answered by Penny Nom. 





An array of pennies 
20030523 

From Saundra: If you have 100 pennies and you are suppose to make an array do you arrange the pennies by date? Answered by Penny Nom. 





1575 
20030313 

From Sharyn: find 6 integers that when multiplied with each other equal +1575 and when the same integers are added together equal zero. there are more positives than negatives and one of the numbers is a double digit between 10 and 20 Answered by Penny Nom. 





X times Y equals ten million 
20030226 

From Baneen: Would you be able to tell me which two numbers would compute ten million without any number having zeros in it? Answered by Penny Nom. 





Factoring 
20030204 

From Marcin: I am having a really hard time with the factor theorem. Can you please help me with the following? (a'3 means a to the exponent 3)
a)8a'3+64b'3c'6 b)8x'412x'344x'2+24x c)x'421x'2100
Answered by Penny Nom. 





Factoring a trinomial 
20030126 

From A student: how do you factor: Xsquared + 8x + 12 Answered by Penny Nom. 





Some 5th grade problems 
20030124 

From Sabrina:
[What is the greatest common factor of 20,28, and 36?] next problem is [5k+7(k+8)= ] next problem [Curtis simplified 0.8 divided by 0.2 x 0.04 and got 10. Latoya Simplified and got 1.6. is either correct? Can you explaine how you got the answer please.] Answered by Penny Nom. 





The least common denominator 
20030121 

From Brittan: Hi there I need help! My name is Brittany and i am in the 6th grade. I need help finding the least common denominator(LCD), and the book says Find the LCM of the denominators and i've done that and then it says write equivalent fractions,using the LCM as the least commonn denominator.The directions say Use the LCD to write each pair as like fractions. and the problem is 1/8 and 5/40. Could u explain how in the word u do this? Thanks a lot Brittany Answered by Penny Nom. 





Factoring 
20021211 

From Larry: Question:
how do u factor trinonmials
EX: X^{ 3} + Y^{ 3}
X^{ 3}  8Y^{ 3}
8X^{ 2}  72
64A^{ 3}  125B^{ 6} Answered by Penny Nom. 





Factoring a cubic 
20021205 

From Dorota: I got a problem with factorise the expression 2x^{3}+11x^{2}5x50. Answered by Penny Nom. 





65,125 
20021204 

From Brittany: I am a threedigit number.When you reverse my digits,a larger number is formed.the product of me and the new number is 65,125.What number am I. Answered by Chris Fisher and Claude Tardif. 





Factor completely 
20021121 

From Shelley: these two questions are to be factored completely but i have no idea how to factor them  (x4y)^{ 2}  3(x4y)  4
 x^{ 6} + y^{ 6}
Answered by Penny Nom. 





Composites, primes, factors and common factors 
20021120 

From Connie: My son can't remember what a composite number is, what a prime number is and the explaination of factors and common factors. Help! Answered by Penny Nom. 





Two problems 
20021014 

From Eva:
a) How many different equivalence relations can be defined on the set X={a,b,c,d}? b)Show that 6 divides the product of any 3 consecutive integers. I know it is true that 6 divides the product of any 3 consecutive integers. However, i have problem showing the proof. Answered by Leeanne Boehm and Penny Nom. 





Three algebra problems 
20021013 

From Veronica: Solve the following inequality: 5(xsqured4)/(xto the 5th(2x5)to the 3rd) < or equal 0 Solve the following equations for all roots square root of x+2=1+square root of 2x+3 what's ZERO FACTOR PROPERTY??? The hypotenuse of an isosceles right triangle is 7cm. long. Determine the lenghts of the other sides. Answered by Leeanne Boehm. 





The factor theorem 
20020910 

From Yael: Prove (x  a  b) is a factor of x^{3}  a^{3}  b^{3}  3ab (a + b) Answered by Penny Nom. 





A limit 
20020903 

From Circe:
Lim 3x^{ 3}+ax+a+3 /(x^{ 2}+x2), X>2 Answered by Penny Nom. 





When is 1! + 2! + 3! + ... + x! a square? 
20020819 

From Sarathy: Solve : 1! + 2! + 3! + ... + x! = y^{ 2} How do i find the solutions ? Answered by Claude tardif. 





Factor 12x^2  20x  8 
20020430 

From Crystal: Factor Completely: 12x^{2}  20x  8 Answered by Penny Nom. 





A polynomial 
20020414 

From A student: A polynomial function is described by the following conditions: f(x) has two real zeros at x= 2 and x= 1, each of multiplicity 2 f(x) has two complex zeros as x goes to infinity, f(x) goes to +infinity as x goes to +infinity, f(x) goes to +infinity f(x) has a yintercept at (0,2) Sketch a polynomial function that satisfies the above conditions. Write an equation for function f(x) Write another function g(x) that also satisfies the above parameters. Answered by Penny Nom. 





24x^4 + 3x 
20020318 

From gary: 24x^{ 4} + 3x Answered by Penny Nom. 





Factor completely 
20020307 

From Taylor: I'm supposed to completely factor this but I don't know what to do with all the variables. a^{3}b^{5}  a^{2}b^{5}  12ab^{5}. Does it have anything to do with b^{5} being a common factor or am I completely off? Answered by Penny Nom. 





A degree 5 polynomial 
20020217 

From Carla: Write an equation for a polynomial of degree 5 given the following zeros: 7+3i, 2+sqrt(13), 6 Answered by Penny Nom. 





Reduce 79,537/3,623,420 
20011213 

From Eliana: How do you reduce 79,537/3,623,420. Answered by Claude Tardif. 





A cubic 
20011110 

From Louise: x^{3} + 9x^{2}  7x  63 Answered by Penny Nom. 





GCD and LCM 
20010924 

From David: Find the GCD adn LCM of the following numbers. Assume p 2 to the power p, 3 to power q, 5 to power r and 2 to power q, 3 to power r, 7 to power p Answered by Penny Nom. 





4x(2x1)+(2x1)^{2} 
20010917 

From Nick: how do u solve 4x(2x1)+(2x1)^{2} Answered by Penny Nom. 





A factoring problem 
20010614 

From A student: What is the factoring of x squared 7+6 equal Answered by Penny Nom. 





Primes and square roots 
20010614 

From Paul: I have a bit of a math problem. It has to do with determining if a very large number is a prime. One method entails dividing the number by every smaller prime number. If any divide into it, it's not a prime. This would be a big job if the number was something like 400 digits long. Another way I read about was to take the square root of the number and test all the primes less than its square root. The explanation went like this: "When a number is divided by another number that is greater than its square root, the result is a number smaller than the square root. For example, the square root of 36 is 6. Dividing 36 by 2, a smaller number than 6, gives 18, a number that is larger than the square root. To prove that 37 is prime it is only necessary to divide it by primes less than 6, since if it had a prime factor greater than 6, it would have to have one less than 6 as well." I understand the explanation, up to the last sentence. I fail to see the underlying logic. Why if a prime factor exists below the square does one have to exist above the square too? The number 40 can be divided by the prime 2, a number below its square root, but no other primes can do this above its square root. Have I missed something? What's the logic here? Answered by Claude Tardif and Penny Nom. 





25 y^2 + 20 y z  4 z^2 
20010515 

From Kimmy: i don't know how to factor the trinomial 25y^{2} + 20yz  4z^{2}. I can get it, but i get messed up on getting the minus 4 at the end. all i get is a plus 4. Can it even be factored. Answered by Penny Nom. 





Greatest Common Factor 
20010509 

From Nicole: What is the Greatest Common Facter for:
126,261 1008,1080 546,1995 128,256 and 255,256 Answered by Penny Nom. 





Factoring 
20010322 

From Kaleena: Factor this equation: 5x^{7}10x^{5}+4x^{3}8x Answered by Harley Weston. 





Difference of squares 
20010220 

From Janna: Hi! I was just wondering how you would factor x^{2}  9y^{2}. Answered by Harley Weston. 





Why is 0! = 1? 
20010130 

From Diane: Every math book always claims that 1!=1 and 0!=1 are givens, and that we should just memorize it. i understand the 1! part, but where is the basis for claiming that 0!=1???? Answered by Walter Whiteley. 





Factoring 
20010124 

From Danielle: 4(x+1)^{2}+y(x+1) Answered by Penny Nom. 





Factoring a trinomial 
20010124 

From Kyle: I am an eighth grade student.I can not figure out the following problem. 4x^{2} + 2x  20 Answered by Leeanne Boehm. 





What number from 1 to 25 has the most factors? 
20010123 

From John: What number from 1 to 25 has the most factors? Answered by Penny Nom. 





Greatest common factor 
20010117 

From A teacher: I'm a teacher at a local Middle School and I would like the answers for the following questions. What is the greatest common factor for.. 546 and 780 156 and 732 . . . Answered by Leeanne Boehm and Penny Nom. 





Compression by a factor of ? 
20010112 

From Wayne: Given an equation like y = (1/2) (x3)^{2} + 6, when describing the distortion from the base curve y = x^{2} is it correct to say there is a vertical compression by a factor of 2, or by a factor of 1/2 ? Which is more correct? I have seen both versions in different high school texts, and I am now unsure which is more correct. Answered by Harley Weston. 





Four crayons 
20010110 

From Neyra Espinoza: You have four crayons (red, blue, yellow, green). If you line them up, how many different combinations can you get? Answered by Patrick Maidorn. 





A pair of numbers whose GCF is 28 
20001227 

From John: Name 2 different pairs of numbers whose GCF is 28. Answered by Penny Nom. 





Factoring (uv)^{3}+vu 
20001215 

From A parent: I am a middle school teacher and a parent. I am snowed in and trying to help my 9th grader get ready for 9 weeks exams. I have tried to factor this problem to no avail. (uv)^3+vu. I have the answer but I need to know how it is done. Answered by Penny Nom. 





Prime factorization 
20001213 

From A student: What is the prime factorization for 250 1296 and 2400 Answered by Penny Nom. 





Factoring a cubic 
20001031 

From A student: Factor Completely 18p^{3}  51p^{2}  135p Answered by Paul Betts and Penny Nom. 





A zip code problem 
20001026 

From Rob Mathis: Find the zip code of a place in a county so that the product of it and the zip code of another place in another county of the same name, but in a different state, is an exact multiple of the number 123456789 Answered by Claude Tardif. 





1234567890 
20000914 

From Bradley Kloetzly: Can you find two whole numbers, with the smallest possible difference between them, which when multipled together equal: 1234567890? Answered by Harley Weston. 





Factoring 
20000912 

From Melissa: I would like you to help me factor (x^{ 6}y^{ 6}) & (a+b)^{2}+3(a+b)4 Answered by Penny Nom. 





Roots of x^2 + 22 x + 112 
20000907 

From Brian R.: I need to find the root of the quadratic equation of a square. The problem is x^{2} + 22x + 112 = 0. Answered by Penny Nom. 





n! = 42(n2)! 
20000721 

From Damon Bailey: Solve n! = 42(n2)! Answered by Paul Betts. 





10,000! 
20000721 

From Lauren: Hi I was just wondering if you could tell me how many zeros are in 100,000! (factorial.) Answered by Denis Hanson. 





Factoring trinomials that are squared 
20000417 

From A student: I have a question that I really need an answer to. I need help with factoring trinomials that are squared. Answered by Penny Nom. 





How many zeros? 
20000409 

From Greg Potts: The natural numbers 1 to 25 are multiplied together (1 x 2 x 3x..24 x 25). How many zeros are there in the product of this multiplication? a)6 b)7 c)5 d)10 or e)4? Answered by Harley Weston. 





Six digit numbers using 1,2,5,6,7, and 9 
20000320 

From Rachel: How many different sixdigit numbers can you make using the digits 1,2,5,6,7, and 9? How many of these six digit numbers are divisible by six? Answered by Claude Tardif and Denis Hanson. 





Division 
20000316 

From Charday: What is the easiest way to calculate the least number that can be divided evenly by all the numbers from 1 to 10. Answered by Penny Nom. 





10 000 000 = a x b 
20000306 

From Spencer Jaffe: What two numbers that don't end in zero, multiplied equal 10,000,000. Answered by Claude tardif. 





Factoring, primes, GCF and LCM 
20000227 

From Ruth Kroek: My son is in grade seven, he has to do a Factoring Booklet the areas covered are:  Prime #'s
 Composite #'s
 Rainbow Factoring
 Finding Multiples (consecutive multiples)
 Finding GCF of 23 numbers uning Rainbow factoring
 Finding LCM of 2 numbers using consecutive multiples
 prime factor trees
 prime factor ladders
 finding GCF of 2 numbers using Prime number Method
Although his text 'Math Power' gives some information, we are at a loss .. Answered by Penny Nom. 





Three factors 
20000221 

From A parent: Question from a parent helping a child, grade 4, with homework. Can a number have three factors? Name three numbers that have three factors. Answered by Penny Nom. 





Factors 
20000215 

From Guy Rayfield: Please can you tell me the factors of 6 I think the answer is 2 and 3  am I right? Answered by Penny Nom. 





Factors 
20000127 

From Pam: My son [age 9, 4th grade] has a math problem with factors. I need to know how to do the problem that involves the factor 24. I'm not even sure where to start. Answered by Harley Weston. 





Factoring by graphing 
20000111 

From Dylan Kirkwood: How can you factor a quadratic equation by graphing it? Answered by Penny Nom. 





Factoring ^6 
20000103 

From Athena:
my name is Athena and I have a question on factoring: how would you figure this out: (x^{6}y^{6}) and (x^{6}+y^{6}) Answered by Penny Nom. 





Solving a cubic equation 
19991230 

From Natalia: How can I solve: 2 x^{3}  x^{2} + x  2 = 0 ??? Answered by Penny Nom. 





Two algebra problems 
19991217 

From Michael Standfest: If x+4 is a factor of 2x^{4}+kx^{3}3kx^{2}+6x40, find k and Prove that n^{2}n is even for all n, using the proof of contradiction Answered by Penny Nom. 





order 4+ determinants 
19991206 

From Joe Kron: Why is it never shown how to calculate the value of 4x4 (or larger size) deteminants by the diagonal multiply methods that are generally shown for 2x2 and 3x3 determinants? The method I'm talking about is called Cramer's Rule??? Is this method not extensible to order 4+ and if not why not? Anyway the method always shown for order 4+ is called "reduction by minors" which is not the answer to this question. Answered by Walter Whiteley. 





An odd number of factors 
19991022 

From Melissa: What is the common name used for numbers that have an odd number of factors? What is the least positive integer that has exactly 13 factors? Answered by Penny Nom. 





0! + 1! + 2! + 3! + ... + 2000! 
19991021 

From Melissa: My name is melissa. I am a 9th grade student I am having trouble finding out how to do this: What is the tens digit of 0! + 1! + 2! + 3! + ... + 2000! I know how to find these, but my calculator cant go any higher than 69! Is there any way i can do this problem? Answered by Penny Nom. 





Common factors 
19991006 

From Tommygirl98: Ok I have a question about common factoring I'm not to sure if you could help me but it's worth a try here it goes. Ok I have a test on Friday and i'm having trouble understanding how to do it here's an example, Factor, 10 + 2b how do you do it and what do they mean by factor? Answered by Penny Nom. 





Using Factoring in Problem Solving 
19990909 

From Lori: I have a problem with a problem. The Problem is....The sum of the squares of two consecutive positive even integers is 340. Find the integers. Answered by Penny Nom. 





A difference of squares problem. 
19990724 

From Michael and Stephanie Bixler: If you have the equation x= n^{2}  m^{2} (ie 40= 7^{2}3^{2}= 499) x must = a positive number 1) which squared numbers work as n and m 2) how does it work 3) if my teacher gave me the number for x; how could I figure out this problem Answered by Harley Weston. 





Factoring 
19990330 

From Maggie Stephens: I don't know anything about factoring would you plese help me. 3x^{4}  48 54x^{6} + 16y^{3} 1258x^{3} 12x^{2}  36x + 27 9  81x^{2} a^{3} + b^{3}c^{3} I would greatly appreciate any help you can give me thanks. Answered by Jack LeSage. 





Factoring polynomials 
19990329 

From Karen: I have been unable to factorise a polynomial equation and was wondering if you could please help. It is level (1012) maths. The polynomial is x^{3} + x^{2}  24x + 36 I have tried a few factorisation methods such as foctorisation by grouping but it won't work this polynomial. Please help. Answered by Jeff Walters and Jack LeSage. 





Factoring 
19990308 

From L. Sivad: Question: m^{2}+6m+9n^{2} Answered by Penny Nom. 





Composite Numbers 
19981007 

From Greg Murphy: What type of composite number has an odd number of factors? Answered by Harley Weston. 





Students and Lockers 
19981002 

From Mike: There is a row of 1000 lockers. There is a line of 1000 students. Student number 1 starts at the first locker and opens all 1000. Student number 2 starts at the second locker and closes every other one. Student number 3 starts at the third locker and goes to every third one, closing the open ones and opening the closed ones. Student number 4 does the same with every fourth locker and so on down the line... After all 1000 students have gone how many lockers are open and which ones are they? Please help! There is proboly a simple solution but we couldnt figure it out for the life of us. Please let us know how you solve it. Answered by Patrick Maidorn and Penny Nom. 





Five Factors 
19980919 

From Derek Yau: To whom it may concern, I have difficulty in getting the solution to the following question: Find 5 numbers that have exactly 5 factors. I got 16, 81 but couldn't find the rest. I believe that in order to have 5 factors, it has to be a square number. Isn't it true? I guess there may be a pattern to this. Thanks for your help. Derek Yau. Answered by Penny Nom. 





3 to the power of 1994 
19980905 

From Kim Tangney: What are the last two digits of:  3 to the power of 1994
 7 to the power of 1994
 3 to the power of 1994 + 7 to the power of 1994
 7 to the power of 1994  3 to the power of 1994
Answered by Penny Nom. 





Solving Quadratics 
19980716 

From Fred Goodrich: I need a step by step lesson on solving quadratic equations. Thank you, Answered by Penny Nom. 





Difference of squares 
19980623 

From Kristen Smelsky: Solve the following using a difference of squares: 4x(squared) minus 4xy plus y(squared) minus m(squared) plus 2m minus 1 Answered by Penny Nom. 





The Largest Factor 
19980315 

From Senthuran Nadarajah: When each expression is evaluated for different values of n, the answers will differ. For each expression, find largest natural number that will divide the result for all natural number values of n. n^5  5n^3 + 4n Answered by Harley Weston. 





Divisors of 6n 
19980126 

From James: If n is a positive integer such that 2n has 28 positive divisors and 3n has 30 positive divisors, then how many positive divisors does 6n have? (a) 32 (b) 34 (c) 35 (d) 36 (e) 38 Answered by Penny Nom and Haragauri Gupta. 





The Factor Theorem 
19980118 

From Dhruv Bansal: Hi, I'm a ninth grade student doing a math project for school. I'm trying to learn about various ways of solving 3rd and 4th degree polynomial equations using the remainder theorem, the factor theorem, and synthetic division. The books I have all mention x  r, which I know nothing about, not even how to get it. I would really appreciate any information on this. Thanks. Dhruv Bansal Answered by Penny Nom. 





Greatest Common Factor. 
19980109 

From Percy Stribling: how do you figure out what the greater common factor is? Answered by Penny Nom. 





0! 
19970302 

From Donna D. Hall: I am looking for a quick and easy explanation as to why 0! is 1. Answered by Walter Whiteley and Denis Hanson. 





Divisibility of 2n choose n. 
19960924 

From Kathy Doan: Can you prove that "2n choose n" is not divisible by 3, 5, and 7 for infinitely many n? Answered by Penny Nom. 





Term definitions 
19960918 

From M. Seltzer: A 7th grade algebra student would like the definition of the terms proper factor and perfect number. Answered by The Centralizer. 





Number of factors 
19960130 

From Chrissy: What number has exactly 13 positive factors? Answered by Penny Nom. 

