Answer
$(x+1)(x+12)$
Work Step by Step
The given expression, $
x^2+13x+12
,$ has $c=
12
$ and $b=
13
.$
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 $\{
1,12
\}.$ Hence, the factored form is
\begin{array}{l}\require{cancel}
(x+1)(x+12)
.\end{array}