Answer
$(x+4)(x-16)$
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 $x^2-12x-64$, we are looking for two numbers whose product is $-64$ and whose sum is $-12$. The numbers $-16$ and $4$ meet these criteria, because $$4\times-16=-64\;\text{and}\;-16+4=-12$$When we insert these numbers into the blanks, we arrive at the factors $(x+4)(x-16)$.
