Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases : $p(x)=2 x^{3}+x^{2}-2 x-1$, $g(x)=x+1$.
Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases : $p(x)=2 x^{3}+x^{2}-2 x-1$, $g(x)=x+1$.
We have $p ( x )=2 x ^{3}+ x ^{2}-2 x -1$ and
$g(x) =x+1$
$\therefore$ $p(-1) =2(-1)^{3}+(-1)^{2}-2(+1)+1=2(-1)+1+2-1$
$=-2+1+2-1=-3+3=0$
$\because$ $p (-1)=0$
$\therefore g ( x )$ is a factor of $p ( x )$.
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