Is $x+1$ a factor of $x^3+8x^2+11x-20$ ?

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Answer 1 · 2016-11-08T13:02:29

$(x+1)$ is not a factor, but $(x-1)$ is.

Given $p(x)=x^3+8x^2+11x-20$ if $x+1$ is a factor of $p(x)$ then

$p(x)=(x+1)q(x)$ so for $x=-1$ we must have

$p(-1)=0$

Verifying on $p(x)$

$p(-1)=(-1)^3+8(-1)^2+11(-1)-20=-24$

so $(x+1)$ is not a factor of $p(x)$

but $(x-1)$ is a factor because

$p(1)=1+8+11-20=0$

Is x+1x+1 a factor of x^3+8x^2+11x-20x^3+8x^2+11x-20?