Chapter 5 - Polynomials and Factoring - 5.6 Factoring: A General Strategy - 5.6 Exercise Set - Page 344: 45

$(x+5y)(3x-2y)$

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}