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

$-a^2(a+12)(a-11)$
Factoring the negative $GCF= -a^2$, the given expression, $-a^4-a^3+132a^2 ,$ is equivalent to \begin{array}{l} -a^2(a^2+a-132) .\end{array} The 2 numbers whose product is $ac= 1(-132)=-132$ and whose sum is $b= 1$ are $\left\{ 12,-11 \right\}.$ Using these two numbers to decompose the middle term of the above trinomial, then \begin{array}{l} -a^2(a^2+12a-11a-132) \\\\= -a^2[(a^2+12a)-(11a+132)] \\\\= -a^2[a(a+12)-11(a+12)] \\\\= -a^2[(a+12)(a-11)] \\\\= -a^2(a+12)(a-11) .\end{array}