Answer
$3(x-9)(x+1)$
Work Step by Step
Factoring the $GCF=
3
,$ the given expression, $
3x^2-24x-27
,$ is equivalent to
\begin{align*}
3(x^2-8x-9)
.\end{align*}
Using the factoring of trinomials in the form $x^2+bx+c,$ the expression above has $c=
-9
$ and $b=
-8
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-9,1
\right\}.$ Using these two numbers, the factored form of the expression above is
\begin{align*}
3(x-9)(x+1)
.\end{align*}