#### Answer

$(t+8)(t+2)$

#### 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 $t^2+10t+16$, we are looking for two numbers whose product is $16$ and whose sum is $10$. The numbers $8$ and $2$ meet these criteria, because $$8\times(2)=16\;\text{and}\;8+(2)=10$$When we insert these numbers into the blanks, we arrive at the factors $(t+8)(t+2)$