Answer
$-5(x-1)(x-9)$
Work Step by Step
Factoring the negative $GCF=
-5
,$ the given expression, $
-5x^2+50x-45
,$ is equivalent to
\begin{array}{l}\require{cancel}
-5(x^2-10x+9)
.\end{array}
The trinomial expression above has $c=
9
$ and $b=
-10
.$
The possible factors of $c$ are $
\{ 1,9 \}
,\{ 3,3 \}
\{ -1,-9 \}
,\{ -3,-3 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
-1,-9
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
-5(x-1)(x-9)
.\end{array}