## Intermediate Algebra (6th Edition)

$z(2x-3)(x+4)$
Factoring the $GCF=z$ of the given expression, $2x^2z+5xz-12z$, results to \begin{array}{l}\require{cancel} z(2x^2+5x-12) .\end{array} The two numbers whose product is $ac= 2(-12)=-24$ and whose sum is $b= 5$ are $\{ -3,8 \}$. Using these two numbers to decompose the middle term, then the factored form of the resulting expression, $z(2x^2+5x-12)$,is \begin{array}{l}\require{cancel} z(2x^2-3x+8x-12) \\\\= z[(2x^2-3x)+(8x-12)] \\\\= z[x(2x-3)+4(2x-3)] \\\\= z[(2x-3)(x+4)] \\\\= z(2x-3)(x+4) .\end{array}