Answer
$5a(2b+7)(b-5)$
Work Step by Step
For the polynomial
$$
10ab^2 -15ab -175a=5a(2b^2-3b-35)
$$
we check the factors of $ac=2(-35)=-70$. The only factors that can give the right middle term are $-10$ and $7$, as follows
$$
10ab^2 -15ab -175a=5a(2b^2-3b+35)=5a(2b+7)(b-5)
.$$
