Explain how to factor $\displaystyle x^9 - x^6 -x^3 + 1 $? Thanks for the help!
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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.
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.
You could also use the rational root theorem, although that would take a while.
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).
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