#### Answer

$(x+3)(x+6)$

#### Work Step by Step

In order to factor $x^{2}+9x+18$, we must find a pair of numbers whose product is equal to 18 (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 18 are 1,18, 2,9, and 3,6.
Out of these pairs, the sum of 3 and 6 is equal to 9.
Therefore, $x^{2}+9x+18=(x+3)(x+6)$.