Answer
$(x-5)(x-13)$
Work Step by Step
The given expression, $
y^2-18y+65
,$ has $c=
65
$ and $b=
-18
.$
The possible factors of $c$ are $
\{ 1,65 \}
,\{ 5,13 \}
,\{ -1,-65 \}
,\{ -5,-13 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
-5,-13
\}.$ Hence, the factored form is
\begin{array}{l}\require{cancel}
(x-5)(x-13)
.\end{array}