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

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Answer 1 · 2017-01-16T11:59:38

$(x-1)$ is not a factor of $P(x)$

If $x-1$ were a factor of $P(x)$ then $P(x)=(x-1)q(x)$ and then

$P(1)=(1-1)q(1)=0$ but as can be verified

$P(1)=1-3+1+2=1$ so $(x-1)$ is not a factor of $P(x)$

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