Prove that $x+2$ is a factor of $p(x)=2x^{3}-4x^{2}+5x+42$.

(N/A) According to the Factor Theorem,if $(x-a)$ is a factor of a polynomial $p(x)$,then $p(a)=0$.
Here,we need to check if $(x+2)$ is a factor of $p(x)=2x^{3}-4x^{2}+5x+42$.
Comparing $(x+2)$ with $(x-a)$,we get $a = -2$.
Now,we calculate $p(-2)$:
$p(-2) = 2(-2)^{3} - 4(-2)^{2} + 5(-2) + 42$
$p(-2) = 2(-8) - 4(4) - 10 + 42$
$p(-2) = -16 - 16 - 10 + 42$
$p(-2) = -42 + 42$
$p(-2) = 0$
Since $p(-2) = 0$,by the Factor Theorem,$(x+2)$ is a factor of $p(x)$.