#### Answer

$(x+4)(x+5)$

#### Work Step by Step

In order to factor $x^{2}+9x+20$, we must find a pair of numbers whose product is equal to 20 (or the constant term) and whose sum is equal to 9 (or the coefficient on the middle term).
We know that the pairs of numbers whose product is 20 are 1,20, 2,10, and 4,5.
Out of these pairs, the sum of 4 and 5 is equal to 9.
Therefore, $x^{2}+9x+18=(x+4)(x+5)$.