Answer
$(3x+4)(x+9)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the given expression,
\begin{align*}
3x^2+31x+36
\end{align*}
has $ac=
3(36)=108
$ and $b=
31
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
4,27
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{align*}
3x^2+4x+27x+36
\end{align*}
Grouping the first and second terms and the third and fourth terms, the expression above is equivalent to
\begin{align*}
(3x^2+4x)+(27x+36)
\end{align*}
Factoring the $GCF$ in each group results to
\begin{align*}
x(3x+4)+9(3x+4)
\end{align*}
Factoring the $GCF=
(3x+4)
$ of the entire expression above results to
\begin{align*}
(3x+4)(x+9)
\end{align*}
