Chapter 6 - Section 6.1 - The Greatest Common Factor and Factoring by Grouping - Exercise Set - Page 427: 58

$(x+7)(x+10)$

Factoring the $GCF= (x+7) ,$ the given expression, $ x(x+7)+10(x+7) ,$ is equivalent to \begin{array}{l}\require{cancel} (x+7) \left[ \dfrac{x(x+7)}{(x+7)}+\dfrac{10(x+7)}{(x+7)} \right] \\\\= (x+7) \left[ \dfrac{x\cancel{(x+7)}}{\cancel{(x+7)}}+\dfrac{10\cancel{(x+7)}}{\cancel{(x+7)}} \right] \\\\= (x+7)(x+10) .\end{array}