## Intermediate Algebra (6th Edition)

$2xy(x+3)(x-2)$
Factoring the $GCF=2xy$, then the given expression, $2x^3y+2x^2y-12xy$, is equivalent to \begin{array}{l} 2xy(x^2+x-6) .\end{array} The two numbers whose product is $ac= 1(-6)=-6$ and whose sum is $b= 1$ are $\{ 3,-2 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $2xy(x^2+x-6)$, is \begin{array}{l}\require{cancel} 2xy(x^2+3x-2x-6) \\\\= 2xy[(x^2+3x)-(2x+6)] \\\\= 2xy[x(x+3)-2(x+3)] \\\\= 2xy[(x+3)(x-2)] \\\\= 2xy(x+3)(x-2) .\end{array}