Answer
$(r-6)(r-7)$
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 $r^2-13r+42$, we are looking for two numbers whose product is $42$ and whose sum is $-13$. The numbers $-6$ and $-7$ meet these criteria, because $$-6\times(-7)=42\;\text{and}\;-6+(-7)=-13$$When we insert these numbers into the blanks, we arrive at the factors: $(r-6)(r-7)$.
