Answer
$(x-1)(x-7)$
Work Step by Step
The given expression, $
y^2-8y+7
,$ has $c=
7
$ and $b=
-8
.$
The possible factors of $c$ are $
\{ 1,7 \}
,\{ -1,-7 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
-1,-7
\}.$ Hence, the factored form is
\begin{array}{l}\require{cancel}
(x-1)(x-7)
.\end{array}