Answer
$(2m-5)(m-3)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the given expression,
\begin{align*}
2m^2-11m+15
\end{align*}
has $ac=
2(15)=30
$ and $b=
-11
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-5,-6
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{align*}
2m^2-5m-6m+15
\end{align*}
Grouping the first and second terms and the third and fourth terms, the expression above is equivalent to
\begin{align*}
(2m^2-5m)-(6m-15)
\end{align*}
Factoring the $GCF$ in each group results to
\begin{align*}
m(2m-5)-3(2m-5)
\end{align*}
Factoring the $GCF=
(2m-5)
$ of the entire expression above results to
\begin{align*}
(2m-5)(m-3)
\end{align*}
