## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$-4(x+3)(3x-2)$
Factoring the $GCF= -4 ,$ the given expression is equivalent to \begin{array}{l}\require{cancel} -12x^2-28x+24 \\\\= -4(3x^2+7x-6) .\end{array} Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{ expression }$ \begin{array}{l}\require{cancel} -4(3x^2+7x-6) \end{array} has $ac= 3(-6)=-18$ and $b= 7 .$ The two numbers with a product of $c$ and a sum of $b$ are $\left\{ 9,-2 \right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to \begin{array}{l}\require{cancel} -4(3x^2+9x-2x-6) .\end{array} Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to \begin{array}{l}\require{cancel} -4[(3x^2+9x)-(2x+6)] .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} -4[3x(x+3)-2(x+3)] .\end{array} Factoring the $GCF= (x+3)$ of the entire expression above results to \begin{array}{l}\require{cancel} -4[(x+3)(3x-2)] \\\\= -4(x+3)(3x-2) .\end{array}