Answer
$(m-3n)(2m+5n)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
2m^2-mn-15n^2
,$ use the factoring of trinomials in the form $ax^2+bx+c.$
$\bf{\text{Solution Details:}}$
In the trinomial expression above, $a=
2
,b=
-1
,\text{ and } c=
-15
.$ Using the factoring of trinomials in the form $ax^2+bx+c,$ the two numbers whose product is $ac=
2(-15)=-30
$ and whose sum is $b$ are $\left\{
-6,5
\right\}.$ Using these two numbers to decompose the middle term results to
\begin{array}{l}\require{cancel}
2m^2-6mn+5mn-15n^2
.\end{array}
Using factoring by grouping, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(2m^2-6mn)+(5mn-15n^2)
\\\\=
2m(m-3n)+5n(m-3n)
\\\\=
(m-3n)(2m+5n)
.\end{array}
