#### Answer

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

#### Work Step by Step

To factor a trinomial in the form $x^2+bx+c$, we must find two numbers whose product is $c$ and whose sum is $b$. We then insert these two numbers into the blanks of the factors $(x+\_)(x+\_)$.
In the case of $x^2+3xy-10y^2$, we are looking for two numbers whose product is $-10y^2$ and whose sum is $3y$. The numbers $5y$ and $-2y$ meet these criteria, because $$5y\times-2y=-10y^2\;\text{and}\;5y+(-2y)=3y$$When we insert these numbers into the blanks, we arrive at the factors $(x+5y)(x-2y)$.