Answer
$(x+3)(x-12)$
Work Step by Step
In order to factor $x^{2}-9x-36$, we must find a pair of numbers whose product is equal to -36 (or the constant term) and whose sum is equal to -9 (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 negative sum.
We know that the pairs of numbers whose product is -36 are -1,36, 1,-36, -2,18, 2,-18, -3,12, 3,-12, -4,9, 4,-9, and 6,-6.
Out of these pairs, the sum of 3 and -12 is equal to -9.
Therefore, $x^{2}-9x-36=(x+3)(x-12)$.
