Answer
$(x+14y)(x-3y)$
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 $x^2+11xy-42y^2$, we are looking for two numbers whose product is $-42y^2$ and whose sum is $11y$. The numbers $14y$ and $-3y$ meet these criteria because $$14y\times-3y=-42y^2\;\text{and}\;14y+(-3y)=11y$$When we insert these numbers into the blanks, we arrive at the factors $(x+14y)(x-3y)$.
