







3 over "x" plus 5 
20150223 

From Kenny: 3 over "x" plus 5. I don't know this is either a polynomial and if so how would you define it. Answered by Harley Weston. 





Two quadratic polynomials 
20141028 

From khushboo: The zeroes of a quadratic polynomial x^2+ax+b are 'c' and 'd'
and the zeroes of a quadratic polynomial x^2+cx+d=0 are 'a' and 'b'.
find the numerical value of a+b+c+d where a, b, c and d are non zero integers. Answered by Penny Nom. 





Multiplying binomials 
20120514 

From Jordan: How do I solve the equation:
3(x+4)(x6) Answered by Penny Nom. 





A quartic polynomial that is a perfect square 
20120205 

From archit: If P(x)=x^4+ax^3+bx^28x+1 is a perfect square then (a+b)=? 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. 





Identify each polynomial by its degree and number of terms 
20110110 

From betty: Write in standard form and identify each polynomial by its degree and number of terms. How do you do this? Answered by Penny Nom. 





A fourth degree polynomial function with real coefficients 
20101030 

From Ryan: Question from Ryan, a student:
What is the fourth degree polynomial function with real coefficients
that has 1,1 and I as zeros and such that f(x)=160 Answered by Harley Weston. 





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. 





Four dots are randomly placed on an 8x8 grid 
20100226 

From bobbym: Four dots are randomly placed on an 8x8 grid, compute the probability
that no row or column contains more than one dot. Answered by Claude Tardif. 





Coefficients 
20091117 

From Da'mon: The Coefficients of the expression 8  5x  4 + 3x are 5 and 3
Whether the statement is true or false. Answered by Penny Nom. 





The roots of a polynomial 
20091103 

From Jess: Find the value of a positive integer k such that f(x)=x^2  2kx + 55 has roots at k +3 and k  3. Answered by Penny Nom. 





The zeros of a polynomial 
20090925 

From jordan: find a polynomial of lowest degree with only real coefficients and having the given zeros.
1+2i, 2 (multiplicity 2) Answered by Penny Nom. 





Fourth and fifth degree polynomials 
20090820 

From Evin: hello.i am a student . ax^4+bx^3+cx^2+dx+e=0 x=? i want to learn the solution or formula of equations of the fourth and fifth degree...PLEASE Answered by Robert Dawson. 





Multiplication of polynomials 
20090407 

From Carla: I am struggling to understand Multiplication of Polynomials. No matter how hard I try to understand Multiplication of Polynomials, I just can't get it!
The problem that I am trying to solve is this :
3x^3y(y + 2 x^2 + x) Answered by Robert Dawson. 





Leading terms and leading coefficients 
20090331 

From Susan: Write the polynomial P(x)=x^33x^4+17x+114/3x^2 in descending order. Identify the leading term and the leading coefficient. Answered by Penny Nom. 





Primes and polynomials 
20081124 

From Andrew: How effective are the two
pairs of polynomials, taken together, at "excluding" any prime p.
1. (a^2  a.b + b^2) and (a^2 + a.b + b^2) Where b > a > p and (a, b, p) = 1
2. (c^2  c.a + a^2) and (c^2  c.b + b^2) Where c > b > a > p and (a, b, c, p) = 1 Answered by Victoria West. 





A question about primes and polynomials 
20081116 

From Andrew: Is it possible for (a^2  a.b + b^2) to be divisible by a prime p where
b > a > p and a, b, and p are relatively prime? I let a = n.p + x and
b = m.p + y (where both x and y are < p) and after dividing throughout
by p one gets to decide whether (x^2  x.y + y^2) ==0 mod(p) ?! It seems
unlikely unless p = (x^2  x.y + y^2)? (Note: All letters represent positive
integers.) Answered by Chris Fisher and Victoria West. 





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. 





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. 





A polynomial equation 
20080418 

From Joan: Find all polynomials P(x) satisfying x^2P(x) + P(1x) = 2xx^4 Answered by Harley Weston. 





5x^2  45 
20080211 

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





Imaginary roots 
20071209 

From Josh: What is the correlation between imaginary roots (of a quadratic or other
polynomial equation) and the graph of the equation? As in, how can one
represent imaginary solutions graphically (and why does that work)? Answered by Harley Weston. 





6(x1)3(x+1)12=56+5x 
20071024 

From Megan: 6(x1)3(x+1)12=56+5x Answered by Penny Nom. 





(5C squared + 14C + 11) divided by (5C + 4) 
20070920 

From John: (5C squared + 14C + 11) divided by (5C + 4) Answered by Harley Weston. 





What is the inverse function of y=x^3 +x? 
20070919 

From saman: what is the inverse function of y=x^3 +x Answered by Harley Weston. 





Cubic polynomials 
20070814 

From Jalon: The cubic function f(x) = (x+2)^3 touches the x axis only once at x = 2 (negative two). it could also be written as f(x) = (x+2)(x+2)(x+2)
Investigate the cubic functions below as well as the one above and comment clearlt and fully on where they touch/intersect the x axis, and how these points relate to the given function.
a) f(x) = (x – 3)(x +4)(x – 2)
b) f(x) = x(x + 1)^2 (^2 = that means it squared)
Your comments should reference graphs illustrating your conclusions and display another 2 trinomial graphs that demonstrate your conclusions. particular attention should be given to the number of times your function crosses or touches the X axis.
i dont know how this works but could you send the answer to..... spongy_91@hotmail.com Answered by Stephen La Rocque. 





A matrix of polynomials 
20070718 

From Mac: can you please help me out to solve this ?
Let A be a n*n matrix, the elements of which are real (or complex) polynomial in x.
If r rows of the determinant becomes identical when x=a, then the determinant
A) has a factor of order r
B) has a factor or order > r
C) has no factor
D) has a factor of order < r Answered by Harley Weston. 





A polynomial with integer coefficients 
20070620 

From Krys: How do I find a polynomial P(x) with integer coefficient that has degree 4 and zeros 12i and 1 (with multiplicity of 2)? 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. 





Rational polynomial expressions 
20070609 

From a student: I have a question that continues to lead me to the answer x/(x  1) but according to my math book, the answer should be 1/(x  1).
Who is right? Who is wrong?
Here is the question:
(x^2  6x  27)/(x^2  11x + 18) DIVIDED by (x^3 + 2x^2  3x)/(x^2  2x) Answered by Stephen La Rocque. 





The lcm of polynomials 
20070531 

From devin: x^38 , x^34, x^2+4x+4 Answered by Penny Nom. 





Division of polynomials 
20070414 

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





Multiplication of polynomial 
20070209 

From John: hello.. i just want to ask how can i solve this?? (2x+3)(6x+8) Answered by Steve La Rocque, Penny Nom and Brennan Yaremko. 





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. 





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. 





A graph with certain properties 
20041122 

From A student: i was asked as a question in coursework to sketch the graph with the following characteristics:
a double root at 3
a pair of imaginary roots
an xintercept at 6
a root at 4 which is not a double root Answered by Penny Nom. 





Polynomials 
20040125 

From Bruce:
A polynomial is defined as
Polynomial functions are functions that have this form:
f(x) = a_{n}x^{n} + a_{n1}x^{n1} + ... + a_{1}x + a_{0}
The value of n must be an nonnegative integer. That is, it must be
whole number; it is equal to zero or a positive integer.
The coefficients, as they are called, are a_{n}, a_{n1},
..., a_{1}, a_{0}. These
are real numbers.
Questions:
 why must n be positive?
 what are some historical facts
about the evolution of the definition?
Answered by Harley Weston. 





Polynomials degree 4 and bigger 
20030626 

From Stephen:
How do I show kids how to find all the zeros for polynomials degree 4 and bigger.
For examples: r(x) = x^{5}11x^{3}7x^{2}+77 = (x^{2}11)(x^{3}7) and s(x) = x^{4}121 = (x^{2}11)(x^{2}+11) Also am I correct when I say that the following are irreducible? f(x) = x^{2}11 g(x) = x^{3}7 h(x) = x^{4}5 Answered by Harley Weston. 





The HCF and LCM of polynomials 
20030520 

From Charanpal:
Question: Find the HCF and LCM of the polynomials given below. Verify that he productof these HCF and LCM differs from the product of the polynomials, if at all, by a factor of 1  1x^{2} and x^{3} 1
 1  x^{2} and x^{4}  1
Answered by Penny Nom. 





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 polynomial 
20020605 

From Melissa: I'd like to know what is a polynomial( the definition and an explication)? And is 7x a polynomial? and why? 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. 





Dividing polynomials 
20010219 

From Janna: I have two questions involving dividing polynomials by polynomials. Here's the first one: Two factors of 12a^{4} 39a^{2} + 8a  8a^{3} + 12 are a  2 and 2a + 1. Find the other factors. The other question I'm stuck on is: When 10x^{3} + mx^{2}  x + 10 is divided by 5x3, the quotient is 2x^{2} + nx  2 and the remainder is 4. Find the values of m and n. Answered by Penny Nom. 





Polynomials and exponents 
20010115 

From A student: I am duing a project in math on polynomials and exponents. I need a real life usage of polynomials and exponents for my project. Answered by Penny Nom. 





Subtracting polynomials 
20000513 

From Teresa: I am suppose to subtract the lower polynomial from the one above it. 3a+11b+2f 3a 6b+8f ________________ Answered by Penny Nom. 





polynomial functions 
19991119 

From Quinn:
 Without fully factoring the following show that they all have the same zeros:
I: x^{4}x^{2}+2x+6 II: x^{4}+x^{2}2x6 III: 4x^{4}+4x^{2}8x24 IV: 10x^{4}10x^{2}+20x+60  When P(x)=x^{3}3x^{2}+5x+1 and G(x)=x^{3}2x^{2}x+10 are each divided by(xa) the remainders are equal. At what coordinate point does the graph of P(x) intersect G(x)?
Answered by Walter Whiteley. 





Question about 3rd degree polynomials 
19990423 

From Patrick Bryan: What is the general solution to the equation with the form: a*x^3 + b*x^2 + c*x + d = 0 I have once seen a solution to this a few years ago, but I do not recall if it was a general solution. What I do know, is that you could simplify this equation to: a*x'^3 + p*x' + q = 0... Answered by Doug Farenick. 





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. 





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. 





Polynomials 
19980113 

From Sarah Storkey: Hi, My name is Sarah, My question is at the junior level. My question is, what is a polynomial? Answered by Harley Weston. 





Polynomials 
19971007 

From Sheryl and Jeff: I'm a math teacher in Jerusalem, Israel. I'm teaching about graphing polynomial functions in a precalc class. A student asked me what they're good for. I couldn't give her a good example. Do you have one. Thanks. Answered by Penny Nom. 





Roots of a Polynomial 
19961206 

From Paula Miller: Why is the solution called a "root"? Why not just the "xintercepts"? Answered by Chris Fisher and Harley Weston. 

