Answer
$(t+8)(t+12)$
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 $(t+\_)(t+\_)$.
In the case of $t^2+20t+96$, we are looking for two numbers whose product is $96$ and whose sum is $20$. The numbers $8$ and $12$ meet these criteria because $$8\times12=96\;\text{and}\;8+12=20$$When we insert these numbers into the blanks, we arrive at the factors $(t+8)(t+12).$
