# Factoring a polynomial?

• Aug 9th 2012, 11:55 AM
woahitzme
Factoring a polynomial?
Explain how to factor \$\displaystyle x^9 - x^6 -x^3 + 1 \$? Thanks for the help!
• Aug 9th 2012, 12:12 PM
a tutor
Re: Factoring a polynomial?
You could work with \$\displaystyle y^3-y^2-y+1\$ and notice that when y=-1 the expression is zero so that y+1 is a factor.
• Aug 9th 2012, 12:58 PM
richard1234
Re: Factoring a polynomial?
Think of it as \$\displaystyle (x^9 - x^6) - (x^3 - 1)\$

Which is equal to \$\displaystyle x^6 (x^3 - 1) - (x^3 - 1) = (x^3 - 1)(x^6 - 1)\$.

That can be factored a lot more but I'll leave that to you.
• Aug 9th 2012, 04:16 PM
Mrdavid445
Re: Factoring a polynomial?
You could also use the rational root theorem, although that would take a while.
• Aug 9th 2012, 10:05 PM
richard1234
Re: Factoring a polynomial?
Quote:

Originally Posted by Mrdavid445
You could also use the rational root theorem, although that would take a while.

Yeah, it definitely would. I'd just factor it like I showed (or use a tutor's alternative solution, even though it's less intuitive).