Answer
$(a-4)(2a+1)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
2a^2-7a-4
,$ use the factoring of trinomials in the form $ax^2+bx+c.$
$\bf{\text{Solution Details:}}$
In the trinomial expression above, $a=
2
,b=
-7
,\text{ and } c=
-4
.$ Using the factoring of trinomials in the form $ax^2+bx+c,$ the two numbers whose product is $ac=
2(-4)=-8
$ and whose sum is $b$ are $\left\{
-8,1
\right\}.$ Using these two numbers to decompose the middle term results to
\begin{array}{l}\require{cancel}
2a^2-8a+1a-4
.\end{array}
Using factoring by grouping, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(2a^2-8a)+(1a-4)
\\\\=
2a(a-4)+(a-4)
\\\\=
(a-4)(2a+1)
.\end{array}