Answer
$(x+3)(5x+1)$
Work Step by Step
The two numbers whose product is $ac=
5(3)=15
$ and whose sum is $b=
16
$ are $\{
1,15
\}$. Using these two numbers to decompose the middle term, then the factored form of the given expression, $
5x^2+16x+3
$,is
\begin{array}{l}\require{cancel}
5x^2+15x+x+3
\\\\=
(5x^2+15x)+(x+3)
\\\\=
5x(x+3)+(x+3)
\\\\=
(x+3)(5x+1)
.\end{array}
