Answer
$(x+7)(x+10)$
Work Step by Step
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}