Answer
$(x+3)(x+9)$
Work Step by Step
The given expression, $
r^2+12r+27
,$ has $c=
27
$ and $b=
12
.$
The possible factors of $c$ are $
\{ 1,27 \}
,\{ 3,9 \}
\{ -1,-27 \}
,\{ -3,-9 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
3,9
\}.$ Hence, the factored form is
\begin{array}{l}\require{cancel}
(x+3)(x+9)
.\end{array}