Question

What is/are the factor(s) of $(x^{29}-x^{24}+x^{13}-1)$?

• A. $(x-1)$ only
• B. $(x+1)$ only
• C. $(x-1)$ and $(x+1)$
• D. Neither $(x-1)$ nor $(x+1)$

Answer 1

The correct option is A $(x-1)$ only

$f\left(x\right)=x^{29}-x^{24}+x^{13}-1$
$f\left(1\right)=1-1+1-1=0\Rightarrow (x-1)$ is a factor.
$f(-1)=-1-1-1-1\ne 0\Rightarrow (x-1)$ is not a factor.
$\Rightarrow (x-1)$ is the only factor of given expression.