Answer
$2(x-5)(x+4)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
2x^2-2x-40
,$ factor first the $GCF.$ Then use the factoring of trinomials in the form $x^2+bx+c.$
$\bf{\text{Solution Details:}}$
The $GCF$ of the terms in the given expression is $
2
,$ since it is the greatest expression that can divide all the terms evenly (no remainder.) Factoring the $GCF$ results to
\begin{array}{l}\require{cancel}
2(x^2-x-20)
.\end{array}
In the trinomial expression above, $b=
-1
,\text{ and } c=
-20
.$ Using the factoring of trinomials in the form $x^2+bx+c,$ the two numbers whose product is $c$ and whose sum is $b$ are $\left\{
-5,4
\right\}.$ Using these two numbers, the factored form of the expression above is
\begin{array}{l}\require{cancel}
2(x-5)(x+4)
.\end{array}