#### Answer

$\text{This expression is not factorable using integers.}$

#### 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 $t^2+12t+24$, we are looking for two numbers whose product is $24$ and whose sum is $12$. Unfortunately, there are no integers that meet these criteria, so this expression is not factorable using integers.