Answer
$\text{D}$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the given expression, $
4x^2+15x-4
,$ $ac=
4(-4)=-16
$ and $b=
15
.$
The two numbers with a product of $ac$ and a sum of $b$ are $\left\{
-1,16
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{align*}
4x^2-x+16x-4
.\end{align*}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{align*}
(4x^2-x)+(16x-4)
.\end{align*}
Factoring the $GCF$ in each group results to
\begin{align*}
x(4x-1)+4(4x-1)
.\end{align*}
Factoring the $GCF=
(4x-1)
$ of the entire expression above results to
\begin{align*}
(4x-1)(x+4)
.\end{align*}
Hence, the answer is Choice D.
