Answer
yes, $x=-3$ is a solution
Work Step by Step
Using the Remainder Theorem, the remainder when $P(x)=
2x^3-x^2-13x+24
,$ is divided by $(
x+3
)$ is given by $
P(-3)
$.
Substituting $x=-3$ in the function above results to
\begin{align*}
P(-3)&=
2(-3)^3-(-3)^2-13(-3)+24
\\&=
2(-27)-(9)-13(-3)+24
\\&=
-54-9+39+24
\\&=
0
.\end{align*}
Since the remainder is equal to $0$, then $(
x+3
)$ evenly divides $P(x)$. Hence, $
x=-3
$ is a solution of $
2x^3-x^2-13x+24
$.
