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53 items are filed under this topic.
3 over "x" plus 5 2015-02-23
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 2014-10-28
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 2012-05-14
From Jordan:
How do I solve the equation:

Answered by Penny Nom.
A quartic polynomial that is a perfect square 2012-02-05
From archit:
If P(x)=x^4+ax^3+bx^2-8x+1 is a perfect square then (a+b)=?
Answered by Penny Nom.
Factoring with fractions 2011-02-15
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.


Answered by Penny Nom.
Identify each polynomial by its degree and number of terms 2011-01-10
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 2010-10-30
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 2010-03-17
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 2010-02-26
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 2009-11-17
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 2009-11-03
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 2009-09-25
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 2009-08-20
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 2009-04-07
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 2009-03-31
From Susan:
Write the polynomial P(x)=x^3-3x^4+17x+11-4/3x^2 in descending order. Identify the leading term and the leading coefficient.
Answered by Penny Nom.
Primes and polynomials 2008-11-24
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 2008-11-16
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 2008-08-19
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 2008-07-02
From RAM:
If the polynomial x4-6x3+16x2-25x+10 is divided by another polynomial x2-2x+k, the remainder comes out to be x+a. Find k and a.
Answered by Janet Cotcher and Harley Weston.
A polynomial equation 2008-04-18
From Joan:
Find all polynomials P(x) satisfying x^2P(x) + P(1-x) = 2x-x^4
Answered by Harley Weston.
5x^2 - 45 2008-02-11
From Tiana:
factor: 5x^2 - 45
Answered by Stephen La Rocque.
Imaginary roots 2007-12-09
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(x-1)-3(x+1)-12=56+5x 2007-10-24
From Megan:
Answered by Penny Nom.
(5C squared + 14C + 11) divided by (5C + 4) 2007-09-20
From John:
(5C squared + 14C + 11) divided by (5C + 4)
Answered by Harley Weston.
What is the inverse function of y=x^3 +x? 2007-09-19
From saman:
what is the inverse function of y=x^3 +x
Answered by Harley Weston.
Cubic polynomials 2007-08-14
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 2007-07-18
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 2007-06-20
From Krys:
How do I find a polynomial P(x) with integer coefficient that has degree 4 and zeros 1-2i and 1 (with multiplicity of 2)?
Answered by Penny Nom.
Simplifying a quartic rational expression using long division 2007-06-14
From Megan:
Answered by Stephen La Rocque and Penny Nom.
Rational polynomial expressions 2007-06-09
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 2007-05-31
From devin:
x^3-8 , x^3-4, x^2+4x+4
Answered by Penny Nom.
Division of polynomials 2007-04-14
From Rajendra:
Find the remainder when x3+3x+1 is divided by x+pi
Answered by Penny Nom.
Factoring polynomials 2007-02-14
From Joe:
I am in the eighth grade, and we are learning the equivalent of Algebra 2. I have no ides how to factor (x-2)(x^2-1)-6x-6 You help is most aprreciated. Thank you! Joe
Answered by Stephen La Rocque.
Multiplication of polynomial 2007-02-09
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+2x-3 is a factor f(x)=x^4+2x^3-7x^2+ax+b 2006-04-06
From Maha:
Given that x2+2x-3 is a factor f(x)=x4+2x3-7x2+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 2006-02-11
From Katie:
If X2 + 4X + 6 is a factor of X4 + rX2 + s, then find the value of r+s?
Answered by Steve La Rocque and Penny Nom.
A graph with certain properties 2004-11-22
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 x-intercept at 6
a root at 4 which is not a double root

Answered by Penny Nom.
Polynomials 2004-01-25
From Bruce:

A polynomial is defined as
Polynomial functions are functions that have this form:
f(x) = anxn + an-1xn-1 + ... + a1x + a0
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 an, an-1, ..., a1, a0. These are real numbers.


  1. why must n be positive?
  2. what are some historical facts about the evolution of the definition?

Answered by Harley Weston.
Polynomials degree 4 and bigger 2003-06-26
From Stephen:

How do I show kids how to find all the zeros for polynomials degree 4 and bigger.

For examples:
r(x) = x5-11x3-7x2+77 = (x2-11)(x3-7) and s(x) = x4-121 = (x2-11)(x2+11)

Also am I correct when I say that the following are irreducible?

f(x) = x2-11
g(x) = x3-7
h(x) = x4-5

Answered by Harley Weston.
The HCF and LCM of polynomials 2003-05-20
From Charanpal:

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

  1. 1-x2 and x3 -1
  2. 1 - x2 and x4 - 1

Answered by Penny Nom.
The factor theorem 2002-09-10
From Yael:
Prove (x - a - b) is a factor of x3 - a3 - b3 - 3ab (a + b)
Answered by Penny Nom.
A polynomial 2002-06-05
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 2002-02-17
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 2001-02-19
From Janna:
I have two questions involving dividing polynomials by polynomials.

Here's the first one:

Two factors of 12a4 -39a2 + 8a - 8a3 + 12 are a - 2 and 2a + 1. Find the other factors. The other question I'm stuck on is: When 10x3 + mx2 - x + 10 is divided by 5x-3, the quotient is 2x2 + nx - 2 and the remainder is 4. Find the values of m and n.

Answered by Penny Nom.
Polynomials and exponents 2001-01-15
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 2000-05-13
From Teresa:
I am suppose to subtract the lower polynomial from the one above it.
-3a- 6b+8f

Answered by Penny Nom.
polynomial functions 1999-11-19
From Quinn:
  1. Without fully factoring the following show that they all have the same zeros:

    I: x4-x2+2x+6
    II: -x4+x2-2x-6
    III: -4x4+4x2-8x-24
    IV: 10x4-10x2+20x+60

  2. When P(x)=x3-3x2+5x+1 and G(x)=x3-2x2-x+10 are each divided by(x-a) 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 1999-04-23
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 1999-03-29
From Karen:
I have been unable to factorise a polynomial equation and was wondering if you could please help. It is level (10-12) maths. The polynomial is x3 + x2 - 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 1998-01-18
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 1998-01-13
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 1997-10-07
From Sheryl and Jeff:
I'm a math teacher in Jerusalem, Israel.

I'm teaching about graphing polynomial functions in a pre-calc 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 1996-12-06
From Paula Miller:
Why is the solution called a "root"? Why not just the "x-intercepts"?
Answered by Chris Fisher and Harley Weston.



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