Answer
$(x-3)(x-4)$
Work Step by Step
The given expression, $
x^2-7x+12
,$ 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 is
\begin{array}{l}\require{cancel}
(x-3)(x-4)
.\end{array}