Answer
$3(x-2)(x-9)$
Work Step by Step
Factoring the $GCF=
3
,$ the given expression, $
3x^2-33x+54
,$ is equivalent to
\begin{array}{l}\require{cancel}
3(x^2-11x+18)
.\end{array}
The trinomial expression above has $c=
18
$ and $b=
-11
.$
The possible factors of $c$ are $
\{ 1,18 \}
,\{ 2,9 \}
,\{ 3,6 \}
,\{ -1,-18 \}
,\{ -2,-9 \}
,\{ -3,-6 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
-2,-9
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
3(x-2)(x-9)
.\end{array}
