Answer
$(x+15)(x+6)$
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 $x^2+21x+90$, we are looking for two numbers whose product is $90$ and whose sum is $21$. The numbers $15$ and $6$ meet these criteria, because $$15\times6=90\;\text{and}\;15+6=21$$When we insert these numbers into the blanks, we arrive at the factors $(x+15)(x+6)$.
