Chapter 6 - Section 6.2 - Factoring Trinomials Whose Leading Coefficient is 1 - Exercise Set - Page 436: 15

$(x-3)(x+13)$

The given expression, $ y^2+10y-39 ,$ has $c= -39 $ and $b= 10 .$ The possible factors of $c$ are $ \{ 1,-39 \} ,\{ 3,-13 \} ,\{ -1,39 \} ,\{ -3,13 \} $. Among these factors, the pair whose sum is equal to $b$ is $\{ -3,13 \}.$ Hence, the factored form is \begin{array}{l}\require{cancel} (x-3)(x+13) .\end{array}