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

$2(a-7)(a+5)$
Factoring the $GCF= 2$, the given expression, $2a^2-4a-70 ,$ is equivalent to \begin{array}{l} 2(a^2-2a-35) .\end{array} The 2 numbers whose product is $ac= 1(-35)=-35$ and whose sum is $b= -2$ are $\left\{ -7,5 \right\}.$ Using these two numbers to decompose the middle term of the above trinomial, then \begin{array}{l} 2(a^2-7a+5a-35) \\\\= 2[(a^2-7a)+(5a-35)] \\\\= 2[a(a-7)+5(a-7)] \\\\= 2[(a-7)(a+5)] \\\\= 2(a-7)(a+5) .\end{array}