Chapter 6 - Section 6.2 - Factoring Trinomials Whose Leading Coefficient is 1 - Exercise Set - Page 436: 29

$(x-5)(x-13)$

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}