# Is x-1 a factor of P(x)=x^567-3x^400+x^9+2?

$\left(x - 1\right)$ is not a factor of $P \left(x\right)$
If $x - 1$ were a factor of $P \left(x\right)$ then $P \left(x\right) = \left(x - 1\right) q \left(x\right)$ and then
$P \left(1\right) = \left(1 - 1\right) q \left(1\right) = 0$ but as can be verified
$P \left(1\right) = 1 - 3 + 1 + 2 = 1$ so $\left(x - 1\right)$ is not a factor of $P \left(x\right)$