#### Answer

$(x-2)(x+12)$

#### Work Step by Step

In order to factor $x^{2}+10x-24$, we must find a pair of numbers whose product is equal to -24 (or the constant term) and whose sum is equal to 10 (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 -24 are -1,24, 1,-24, -2,12, 2,-12, -3,8, 3,-8, -4,6, and 4,-6.
Out of these pairs, the sum of -2 and 12 is equal to 10.
Therefore, $x^{2}+10x-24=(x-2)(x+12)$.