Answer
a factor
Work Step by Step
Equate $x+3$ to zero then solve for $x$:
\begin{align*}
x+3&=0
\\
x&=-3
\end{align*}
Substituting $x=
-3
$ in the given expression, $
x^3+4x^2+x-6
,$ results to
\begin{align*}
&
(-3)^3+4(-3)^2+(-3)-6
\\&=
-27+4(9)-3-6
\\&=
-27+36-3-6
\\&=
0
.\end{align*}
Since the substitution above is equal to zero, then the remainder is zero. By the Factor Theorem, $
x+3
$ is a factor of $x^3+4x^2+x-6$.
