Explain how to factor $\displaystyle x^9 - x^6 -x^3 + 1 $? Thanks for the help!

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- Aug 9th 2012, 11:55 AMwoahitzmeFactoring a polynomial?
Explain how to factor $\displaystyle x^9 - x^6 -x^3 + 1 $? Thanks for the help!

- Aug 9th 2012, 12:12 PMa tutorRe: 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 PMrichard1234Re: 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 PMMrdavid445Re: Factoring a polynomial?
You could also use the rational root theorem, although that would take a while.

- Aug 9th 2012, 10:05 PMrichard1234Re: Factoring a polynomial?