You are here:

Algebra/Algebra 2 - Polynomials

Question
Need this factored x^5-2x^4+2x

I began by factoring out x^2(x^3-2x^2+2), but need the second polynomial factored down now. Will be 5 total roots (of which, + or - zero I think are two of them) Imaginary numbers are OK, just use i. Please use fractions only, no decimals!

Hi Dakota, I will be happy to help.

Now, you said you factored out a x^2.  As shown here, the last term is 2x, not 2x^2 so you can at most factor an x.

First, factor out the x to get

x(x^4 - 2x^3 + 2)

In order to determine if x^4 - 2x^3 + 2 can be factored, determine if any of the factors, both positive and negative, of 2 are roots by plugging them into the expression and evaluating to see if any come to equal 0.

The only factors of 2 are: -2, -1, 1, 2
Using a calculator, you will find, after plugging these values in, none of the factors are roots.

Therefore the expression is factored completely
x(x^4 - 2x^3 + 2)

I will also look at factoring x*5 - 2x^4 + 2x^2 just in case there was a typo.
Factoring out the x^2 gets

x^2(x^3 - 2x^2 + 2)

Again, the factors of 2 are: -2, -1, 1, 2
However, using these values, none are a root, so the expression is factored completely.

I'm glad I can be of assistance.
Please let me know if you have any questions.
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Fantastic!

Algebra

Volunteer

Anne Losch

Expertise

Solving equations, graphing, evaluatin equations, factoring, functions, systems of equations, rational equations, exponent, complex numbers, word problems, logarithms, polynomials, and all topics in an Algebra 1, Algebra 2, or College Algebra class

Experience

I have a teaching certificate, I have taught Algebra 1 & 2 as well as tutored those subjects and tutored in College Algebra.

Organizations
NEA, past NCTM, MAA, AMS, and ASCD

Education/Credentials
I hold a B.S. in mathematics and computer science from an accredited university and have gone back to school to get my teacher certificate. I hold more than enough credits for an education minor.

Past/Present Clients
I have worked at tutoring centers including Sylvan Learning and Huntington Learning Center. I have posted answers to mathematical questions on answers.com but would rather volunteer with AllExperts.