Answer
$(x+2)(x+5)$
Work Step by Step
The given expression, $
x^2+7x+10
,$ has $c=
10
$ and $b=
7
.$
The possible factors of $c$ are $
\{ 1,10 \}
,\{ -1,-10 \}
,\{ 2,5 \}
,\{ -2,-5 \}
$. Among these factors, the pair whose sum is equal to $b$ are $\{
2,5
\}.$ Hence, the factored form is
\begin{array}{l}\require{cancel}
(x+2)(x+5)
.\end{array}
