Chapter 6 - Section 6.2 - Factoring Trinomials Whose Leading Coefficient is 1 - Exercise Set - Page 436: 12

$(x-1)(x-7)$

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}