Answer
$(x+5)(x+16)$
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 $x^2+21x+80$, we are looking for two numbers whose product is $80$ and whose sum is $21$. The numbers $5$ and $16$ meet these criteria, because $$5\times16=80\;\text{and}\;5+16=21$$When we insert these numbers into the blanks, we arrive at the factors $(x+5)(x+16)$.
