## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$(x+5y)(3x-2y)$
The two numbers whose product is $ac= 3(-10)=-30$ and whose sum is $b= 13$ are $\{ 15,-2 \}$. Using these two numbers to decompose the middle term of the given expression, $3x^2+13xy-10y^2 ,$ then the factored form is \begin{array}{l} 3x^2+15xy-2xy-10y^2 \\\\= (3x^2+15xy)-(2xy+10y^2) \\\\= 3x(x+5y)-2y(x+5y) \\\\= (x+5y)(3x-2y) .\end{array}