Answer
$(x+2)(x+7)$
Work Step by Step
The given expression, $
x^2+9x+14
,$ has $c=
14
$ and $b=
9
.$
The possible factors of $c$ are $
\{ 1,14 \}
,\{ -1,-14 \}
,\{ 2,7 \}
,\{ -2,-7 \}
$. Among these factors, the pair whose sum is equal to $b$ are $\{
2,7
\}.$ Hence, the factored form is
\begin{array}{l}\require{cancel}
(x+2)(x+7)
.\end{array}