Answer
$(4m-3)(6m+5)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the expression
\begin{align*}
24m^2+2m-15
\end{align*} has $ac=
24(-15)=-360
$ and $b=
2
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-18,20
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{align*}
24m^2-18m+20m-15
.\end{align*}
Grouping the first and second terms and the third and fourth terms, the expression above is equivalent to
\begin{align*}
(24m^2-18m)+(20m-15)
.\end{align*}
Factoring the $GCF$ in each group results to
\begin{align*}
6m(4m-3)+5(4m-3)
.\end{align*}
Factoring the $GCF=
(4m-3)
$ of the entire expression above results to
\begin{align*}
(4m-3)(6m+5)
.\end{align*}
Hence, the factored form of $
24m^2+2m-15
$ is $
(4m-3)(6m+5)
$.
