Answer
$-(x-5)(x+9)$
Work Step by Step
Factoring the negative $GCF=
-1
,$ the given expression, $
-x^2-4x+45
,$ is equivalent to
\begin{array}{l}\require{cancel}
-(x^2+4x-45)
.\end{array}
The trinomial expression above has $c=
-45
$ and $b=
4
.$
The possible factors of $c$ are $
\{ 1,-45 \}
,\{ 3,-15 \}
,\{ 5,-9 \}
,\{ -1,45 \}
,\{ -3,15 \}
,\{ -5,9 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
-5,9
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
-(x-5)(x+9)
.\end{array}
