Chapter 5 - Polynomials and Factoring - 5.2 Factoring Trinomials of the Type x2+bx+c - 5.2 Exercise Set - Page 317: 33

$-5(b+10)(b-3)$

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}