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

$4(x+9)(x-4)$
Factoring the $GCF= 4$, then the given expression, $4x^2+20x-144$ is equivalent to \begin{array}{l} 4(x^2+5x-36) .\end{array} The two numbers whose product is $ac= 1(-36)=-36$ and whose sum is $b= 5$ are $\{ 9,-4 \}$. Using these two numbers to decompose the middle term of the trinomial above, then the complete factored form is \begin{array}{l} 4(x^2+9x-4x-36) \\\\= 4[(x^2+9x)-(4x+36)] \\\\= 4[x(x+9)-4(x+9)] \\\\= 4[(x+9)(x-4)] \\\\= 4(x+9)(x-4) .\end{array}