Question

Does anyone know of any re-useable methods for factoring long polynomials like this 5th degree polynomial?

-2x^5+2x^4+8x^3+8x^2-2x-2

I'm great at finding derivatives but not so good at factoring polynomials

Answer 1

There really arent any fast methods for find the roots of a polynomial of high degree. Your best bet is to use the Rational Roots Theorem and hope you get a hit.

Answer 2

You can try:
\[\frac{\pm factors of constant}{factors of leading term}\]
Then using long division. If you get a zero remainder then its a root. I believe thats what joe is talking about.

Answer 3

In this case, after dividing through by 2, RRT only gives u

plus minus 1 as possibilities, neither of which work.

http://www.wolframalpha.com/input/?i=-2x^5%2B2x^4%2B8x^3%2B8x^2-2x-2

is confirmation, I don't know what sort of algorithm they use for approximating roots.