#### Answer

$(x-6)(x-12)$

#### 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 $x^2-18x+72$, we are looking for two numbers whose product is $72$ and whose sum is $-18$. The numbers $-6$ and $-12$ meet these criteria because $$-6\times-12=72\;\text{and}\;-6+(-12)=-18$$When we insert these numbers into the blanks, we arrive at the factors $(x-6)(x-12)$.