## Intermediate Algebra (6th Edition)

$(x-3y)(2x+y)$
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}