Answer
$3pq(a+6b)(a-5b)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
3a^2pq+3abpq-90b^2pq
,$ factor first the $GCF.$ Then use the factoring of trinomials in the form $x^2+bx+c.$
$\bf{\text{Solution Details:}}$
The $GCF$ of the terms in the given expression is $
3pq
,$ since it is the greatest expression that can divide all the terms evenly (no remainder.) Factoring the $GCF$ results to
\begin{array}{l}\require{cancel}
3pq(a^2+ab-30b^2)
.\end{array}
In the trinomial expression above, $a=
1
,b=
1
,\text{ and } c=
-30
.$ Using the factoring of trinomials in the form $x^2+bx+c,$ the two numbers whose product is $c$ and whose sum is $b$ are $\left\{
6,-5
\right\}.$ Hence, the factored form of the expression above is
\begin{array}{l}\require{cancel}
3pq(a+6b)(a-5b)
.\end{array}
