Answer
$-(x-5)(x+8)$
Work Step by Step
Factoring the negative $GCF=
-1
,$ the given expression, $
-x^2-3x+40
,$ is equivalent to
\begin{array}{l}\require{cancel}
-(x^2+3x-40)
.\end{array}
The trinomial expression above has $c=
-40
$ and $b=
3
.$
The possible factors of $c$ are $
\{ 1,-40 \}
,\{ 2,-20 \}
,\{ 4,-10 \}
,\{ 5,-8 \}
,\{ -1,40 \}
,\{ -2,20 \}
,\{ -4,10 \}
,\{ -5,8 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
-5,8
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
-(x-5)(x+8)
.\end{array}