Answer
$2(a-7)(a+5)$
Work Step by Step
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}
