Answer
$(3p+2x)(5p+2x)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
15p^2+16px+4x^2
\end{array} has $ac=
15(4)=60
$ and $b=
16
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
10,6
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
15p^2+10px+6px+4x^2
.\end{array}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(15p^2+10px)+(6px+4x^2)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
5p(3p+2x)+2x(3p+2x)
.\end{array}
Factoring the $GCF=
(3p+2x)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(3p+2x)(5p+2x)
.\end{array}
