Answer
$(x+1)(x+8)
$
Work Step by Step
The given expression, $
x^2+9x+8
,$ has $c=
8
$ and $b=
9
.$
The possible factors of $c$ are $
\{ 1,8 \}
,\{ -1,-8 \}
,\{ 2,4 \}
,\{ -2,-4 \}
$. The factors whose sum is equal to $b$ are $\{
1,8
\}.$ Hence, the factored form is
\begin{array}{l}\require{cancel}
(x+1)(x+8)
.\end{array}