Answer
$(x-5)(x-8)$
Work Step by Step
The given expression, $
x^2-13x+40
,$ has $c=
40
$ and $b=
-13
.$
The possible factors of $c$ are $
\{ 1,40 \}
,\{ 2,20 \}
,\{ 4,10 \}
,\{ 5,8 \}
,\{ -1,-40 \}
,\{ -2,-20 \}
,\{ -4,-10 \}
,\{ -5,-8 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
-5,-8
\}.$ Hence, the factored form is
\begin{array}{l}\require{cancel}
(x-5)(x-8)
.\end{array}