Answer
$(x+3)(3x+5)$
Work Step by Step
The two numbers whose product is $ac=
3(15)=45
$ and whose sum is $b=
14
$ are $\{
5,9
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
3x^2+14x+15
$, is
\begin{array}{l}\require{cancel}
3x^2+9x+5x+15
\\\\=
(3x^2+9x)+(5x+15)
\\\\=
3x(x+3)+5(x+3)
\\\\=
(x+3)(3x+5)
.\end{array}
