Answer
$-5(b+10)(b-3)$
Work Step by Step
Factoring the negative $GCF=
-5
$, the given expression, $
-5b^2-35b+150
,$ is equivalent to
\begin{array}{l}
-5(b^2+7b-30)
.\end{array}
The 2 numbers whose product is $ac=
1(-30)=-30
$ and whose sum is $b=
7
$ are $\left\{
10,-3
\right\}.$ Using these two numbers to decompose the middle term of the above trinomial, then
\begin{array}{l}
-5(b^2+10b-3b-30)
\\\\=
-5[(b^2+10b)-(3b+30)]
\\\\=
-5[b(b+10)-3(b+10)]
\\\\=
-5[(b+10)(b-3)]
\\\\=
-5(b+10)(b-3)
.\end{array}