With the help of the remainder theorem,examine whether $x+2$ is a factor of the polynomial $x^{3}+9x^{2}+26x+24$ or not.

(A) Let $p(x) = x^{3} + 9x^{2} + 26x + 24$ be the given polynomial.
To check if $(x+2)$ is a factor,we find the zero of the linear polynomial $x+2$ by setting $x+2 = 0$,which gives $x = -2$.
According to the factor theorem,if $p(-2) = 0$,then $(x+2)$ is a factor of $p(x)$.
Now,substitute $x = -2$ into $p(x)$:
$p(-2) = (-2)^{3} + 9(-2)^{2} + 26(-2) + 24$
$p(-2) = -8 + 9(4) - 52 + 24$
$p(-2) = -8 + 36 - 52 + 24$
$p(-2) = 60 - 60 = 0$
Since $p(-2) = 0$,by the factor theorem,$(x+2)$ is a factor of $x^{3} + 9x^{2} + 26x + 24$.