







The Polynomial Remainder Theorem 
20190223 

From pasandi: f(x) is a quadratic polynomial. when f(x) is divided by
(x1),(x2) & (x+2) the remainders respectively are 1, 4 and 2 how to find the f(x) in a question like this? Answered by Penny Nom. 





(2018^2019)(2019^2018) 
20190123 

From Nazrul: Find the remainder when (2018^2019)(2019^2018) is divided by 4? Please show me the process. Answered by Harley Weston. 





Division and remainders 
20180412 

From Yogendra: A number is divided by 5,7 and 9. Reminder are 1,2 and 3 respectively.
What is the number?. Give suitable calculations. Answered by Penny Nom. 





Cutting a wire into 18 cm lengths 
20161229 

From Shambhavi: A long wire of some length is cut into small pieces of 216 cm leaves a small piece of length of 89 cm of this part were cut into equal pieces each of 18 cm the length of the left over wire would be Answered by Penny Nom. 





The remainder theorem 
20161004 

From A student: need help with this
f(x)=4x^415x^24; x2
using the remainder theorem to find the remainder Answered by Harley Weston. 





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. 





Remainder 
20141208 

From Muqadasah: A number, when divided by136, leaves remainder 36. If the same number is divided by 17, what will be the remainder? Answered by Penny Nom. 





A 4 digit number 
20140404 

From LIM: "A" is a 4 digit number formed by all the numbers from 1 to 4. When "A" is divided by 9, the remainder is the biggest possible value. What is the biggest value of A? Answered by Chris Fisher. 





Two polynomials are divisible by x  2 
20121226 

From Tehmas: Determine the values of m and n so that the polynomials 2x^3+mx^2+nx3 and x^33mx^2+2nx+4 are both divisible by x2. Answered by Penny Nom. 





The remainder theorem 
20120325 

From Victoria: When k^2 + 3kx + 13k +k^2x  3x^2 is divided by (x4) the remainder is 22. Find the value(s) of K. Answered by Penny Nom. 





Remainders 
20120318 

From Leslie: Question: Janice has some marbles. When she divides them into groups of 4, she has 2 marbles left over. If she divides them into groups of 5, she will also have 2 left over. What is the least number of marbles she can have? Answered by Penny Nom. 





The 10000th day of her life 
20120221 

From derrick: Ella was born early in the morning on a Friday.She got married on the 10000th day of her life. What day of the week was it? Answered by Penny Nom. 





A polynomial remainder 
20101225 

From Asterdine: When a polynomial f(x) is divided by x+1 and x+2, the remainders are 3 and 7 respectively. Find the remainder when f(x) is divided by (x+2)(x+1). Answered by Penny Nom. 





A remainder of 3 
20101124 

From khodr: find the smallest number (>3) that , when divided by 6 , 8 , 15 , and 18 , gives a remainder of 3 . Answered by Robert Dawson. 





Remainders 
20100717 

From GARY: WHAT NUMBER DIVIDED BY 11 LEAVES 1, DIVIDED BY 13 LEAVES 8, AND DIVIDED BY 17 LEAVES 3. Answered by Chris Fisher. 





Counting by sevens 
20100413 

From Larry: Lee counted by 7's beginning with one of the whole numbers from 1 through 7, until Lee passed 1000. If Lee counted
three of the following numbers, which number did Lee NOT count?
a. 107
b. 184
c. 534
d. 641
Answered by Robert Dawson and 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. 





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. 





Divisibility 
20090617 

From Sophia: Hello
Please help my son with the solutions to the following:
a) Determine the remainder when 2^2009 + 1 is divided by 17;
b) Prove that 30^99 + 61^100 is divisible by 31;
c) It is known that numbers p and 8p^2+1 are primes. Find p.
Again, your assistance is greatly appreciated.
Thanks
Sophia Answered by Robert Dawson. 





Thirtytwo divided by 3 
20090402 

From Shelly: x = 32/3
x = 10 2/3 Divide 32 by 3: 32 / 3 = 10 R2.
What I don't get is why is it that 10 with a remainder of 2 ( 10 R2 ) equals 10 2/3? shouldn't it be 10 2/10 ????? Answered by Robert Dawson. 





Finding an Unknown Integer Given Quotients and Remainders 
20081205 

From Mark: What is the least positive integer meeting each of the following conditions?
Dividing by 7 gives a remainder of 4.
Dividing by 8 gives a remainder of 5.
Dividing by 9 gives a remainder of 6. Answered by Janice Cotcher. 





A remainder of 8 
20081202 

From Dawn: when dividing a 3digit number by a 1digit number, for what divisors can you get a reminder of 8 ? Explain Answered by Chris Fisher. 





A remainder of 8 
20081023 

From Kathy: When dividing a 3 digit number by a 1 digit number, for what divisors can you get a remainder of 8? is the question in my son's math book. After searching this web site, how do you explain an answer so that a ten year old can understand? I somewhat understand the answers given, but am afraid my son might not understand the answer? Help??? Answered by Penny Nom. 





Polynomial division and remainders 
20080702 

From RAM: If the polynomial x46x3+16x225x+10 is divided by another polynomial x22x+k, the remainder
comes out to be x+a. Find k and a. Answered by Janet Cotcher and Harley Weston. 





Remainders 
20080630 

From vivek: what is the remainder when 2050*2071*2095 is divided by 23 ?
this question needs to be done in as less time as possible. Answered by Penny Nom. 





Find the smallest number that leaves a remainder of 10 when divided into 90. 
20080624 

From Peter: Find the smallest number that leaves a remainder of 10 when divided into 90. Answered by Janice Cotcher. 





A problem with numbers 
20080518 

From Peter: When a certain number N is divided by d, the remainder is 7. If the original number N is multiplied by 5 and then divided by d, the remainder is 10, find d Answered by Stephen La Rocque and 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. 





Division of polynomials 
20070414 

From Rajendra: Find the remainder when x3+3x+1 is divided by x+pi Answered by Penny Nom. 





What is the remainder when 3^2007 is divided by seven? 
20070218 

From Chris: What is the remainder when 3^2007 is divided by seven?? Answered by Leeanne Boehm. 





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. 





A remainder of 1 
20060913 

From Juan: What is the smallest counting number which when divided by any of the numbers 2,3,4,5,6,,7,8,9 and 10, leaves a remainder of 1? Answered by Paul Betts and Claude Tardif. 





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. 





A fifth degree polynomial 
20060313 

From Forrest: When f(x) = x^{5}  3x^{4}  6x^{3} + 3ax^{2}  24 is divided by x^{2}  2 the remainder is bx.
Find the values of a and b.
Hence solve the equation f(x) = 8x 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. 





For what divisors can you get a remainder of 8? 
20060106 

From Thelma: When dividing a 3 digit number by a 1 digit number, for what divisors can you get a remainder of 8? 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 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. 





An integer x when divided by 5 leaves the remainder 3. 
20050618 

From A teacher: An integer x when divided by 5 leaves the remainder 3. Prove that when 4x is divided by 5, 2 is the remainder Answered by Penny Nom. 





Division names 
20030310 

From A parent: what is the answer to a division problem called Answered by Penny Nom. 





For what divisors can you get a remainder of 8? 
20021113 

From David: When dividing a 3digit number by a 1digit number, for what divisors can you get a remainder of 8? Answered by Penny Nom. 





Piles of coins 
20011205 

From A student: Sharon has less than 20 coins. When she puts them in piles of 5, she has 1 left over. When she put them in piles of 3, she also has 1 left over. How many coins does Sharon have? Answered by Penny Nom. 





A remainder of 1 
20010220 

From A student: what is the smallest positive integer which has a remainder of one when divided by 2,3,4,5 and 6 Answered by Penny Nom. 





Where three sequences meet. 
19990306 

From Ali: My name is Ali and I am in the 5th grade. I have a math question: What is the least positive integer meeting each of the following conditions:  Dividing by 7 gives a remainder of 4
 Dividing by 8 gives a remainder of 5
 Dividing by 9 gives a remainder of 6
Help! Answered by Denis Hanson. 





Pick any odd number, square it, and then divide it by 8 
19981127 

From Brenda Meagher: Pick any odd number, square it, and then divide it by 8. No matter what odd number is chosen and squared and divided by 8, the remainder is one. Could you please explain this to me or is there a pattern that I am not aware Answered by Harley Weston. 





Dividing a Class 
19981001 

From Tom Barker: My eighth grade niece called with the following homework problem: A teacher wanted to divide her class into equally numbered groups. She tried to divide the class into groups of two, but was one student short. She tried to divide the class into groups of five, but was one student short. She tried to divide the class into groups of seven and was successful. What is the least number of students that were in her class? I know the answer is 49, but don't know how to prove it. I must be getting old if I can't solve eighth grade math problems. Your assistance would be appreciated. Answered by Penny Nom. 





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. 





Two Questions 
19970828 

From Faye Tan: I am a trainee teacher. I would appreciate it very much if you could help me solve the following two problems which I think are meant for students at middle grade. 1. If a hen and a half lays an egg and a half in a day and a half, how many hens are needed to lay a dozen eggs in one day? 2. There are fewer than 200 passengers on a train. If they get off in pairs, one passenger will be without a partner. If they get off in groups of 3 or 4, there will still be one passenger left by himself. However, if they get off in groups of 5, no one will be left by themselves. How many passengers are there on the train? Answered by Penny Nom. 





Mathilde aime la musique et les mathématique. 
20100419 

From Lucas: j'ai un problème pouvait vous m'aider a le résoudre:Mathilde aime la musique et les mathématique.Quand on lui demande combien de CD elle a elle répond "Je ne les ai pas comptés.quand je les groupe 5 par 5 ,il ne m'en reste pas.quand je les groupe 2 par2,il m'en reste 1.quand je les range 6 par 6,il m'en reste 5.je suis surque j'en moins que cinquante."
Peuxtu trouver le nombre de CD de Mathilde?
aider moi svp
ps:je suis en 6ème donc faut pas que se soit trop compliqué Answered by Claude Tardif. 

