Answer
$(x-3y)(2x+y)$
Work Step by Step
The two numbers whose product is $ac=
2(-3)=-6
$ and whose sum is $b=
-5
$ are $\{
-6,1
\}$. Using these two numbers to decompose the middle term, then the factored form of the given expression, $
2x^2-5xy-3y^2
$,is
\begin{array}{l}\require{cancel}
2x^2-6xy+xy-3y^2
\\\\=
(2x^2-6xy)+(xy-3y^2)
\\\\=
2x(x-3y)+y(x-3y)
\\\\=
(x-3y)(2x+y)
.\end{array}
