Answer
$3(x+3)(x+4)$
Work Step by Step
Factoring the $GCF=
3
,$ the given expression, $
3x^2+21x+36
,$ is equivalent to
\begin{array}{l}\require{cancel}
3(x^2+7x+12)
.\end{array}
The trinomial expression above has $c=
12
$ and $b=
7
.$
The possible factors of $c$ are $
\{ 1,12 \}
,\{ 2,6 \}
,\{ 3,4 \}
,\{ -1,-12 \}
,\{ -2,-6 \}
,\{ -3,-4 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
3,4
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
3(x+3)(x+4)
.\end{array}
