Answer
$-3(x-1)(x-11)$
Work Step by Step
Factoring the negative $GCF=
-3
,$ the given expression, $
-3x^2+36x-33
,$ is equivalent to
\begin{array}{l}\require{cancel}
-3(x^2-12x+11)
.\end{array}
The trinomial expression above has $c=
11
$ and $b=
-12
.$
The possible factors of $c$ are $
\{ 1,11 \}
,\{ -1,-11 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
-1,-11
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
-3(x-1)(x-11)
.\end{array}