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

$a^2b(ab+5)(ab-3)$
Factoring the $GCF= a^2b$, then the given expression, $a^4b^3+2a^3b^2-15a^2b$ is equivalent to \begin{array}{l} a^2b(a^2b^2+2ab-15) .\end{array} The two numbers whose product is $ac= 1(-15)=-15$ and whose sum is $b= 2$ are $\{ 5,-3 \}$. Using these two numbers to decompose the middle term of the expression, $a^2b(a^2b^2+2ab-15) ,$ then the factored form is \begin{array}{l} a^2b(a^2b^2+5ab-3ab-15) \\\\= a^2b[(a^2b^2+5ab)-(3ab+15)] \\\\= a^2b[ab(ab+5)-3(ab+5)] \\\\= a^2b[(ab+5)(ab-3)] \\\\= a^2b(ab+5)(ab-3) .\end{array}