Answer
$(3t+4)(2t+9)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c$ method, the expression
\begin{align*}
6t^2+35t+36
\end{align*} has $ac=
6(36)=216
$ and $b=
35
.$
The two numbers with a product of $ac$ and a sum of $b$ are $\left\{
8, 27
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above, we find:
\begin{align*}
6t^2+8t+27t+36
.\end{align*}
Grouping the first and second terms and the third and fourth terms, the expression above is equivalent to
\begin{align*}
(6t^2+8t)+(27t+36)
.\end{align*}
Factoring the $GCF$ in each group results in:
\begin{align*}
2t(3t+4)+9(3t+4)
.\end{align*}
Factoring the $GCF=
(3t+4)
$ of the entire expression above results in:
\begin{align*}
(3t+4)(2t+9)
.\end{align*}
Hence, the factored form of $6t^2+35t+36$ is $
(3t+4)(2t+9)
$.
