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

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Answer 1 · 2017-01-16T11:59:38

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

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

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

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

Is x−1x-1 a factor of P(x)=x567−3x400+x9+2P(x)=x^567-3x^400+x^9+2?