Answer
$(r+9)(r-3)$
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 $r^2+6r-27$, we are looking for two numbers whose product is $-27$ and whose sum is $6$. The numbers $9$ and $-3$ meet these criteria, because $$9\times(-3)=-27\;\text{and}\;9+(-3)=6$$When we insert these numbers into the blanks, we arrive at the factors $(r+9)(r-3)$.
