#### Answer

$(x-6)(x+9)$

#### Work Step by Step

In order to factor $x^{2}+3x-54$, we must find a pair of numbers whose product is equal to -54 (or the constant term) and whose sum is equal to 3 (or the coefficient on the middle term). We know that only a pair of one positive and one negative number will produce a negative product and a positive sum.
We know that the pairs of numbers whose product is -54 are -1,54, 1,-54, -2,27, 2,-27, -3,18, 3,-18, -6,9, and 6,-9.
Out of these pairs, the sum of -6 and 9 is equal to 3.
Therefore, $x^{2}+3x-54=(x-6)(x+9)$.