Answer
$(r+10)(r-4)$
Work Step by Step
To factor a trinomial in the form $r^2+br+c$, 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 $(r+\_)(r+\_)$.
In the case of $r^2+6r-40$, we are looking for two numbers whose product is $-40$ and whose sum is $6$. The numbers $10$ and $-4$ meet these criteria because: $$10\times(-4)=-40\;\text{and}\;10+(-4)=6$$When we insert these numbers into the blanks, we arrive at the factors: $(r+10)(r-4)$.
