Question

When factoring x2−10x−24 ,you need two numbers that multiply to equal -24 and add to -10.

Answer 1

-12 and 2; it is factored as
`(x+2)(x-12)`

Explanation:

Since their product is negative, one is positive and the other is negative.

Moreover, since the sum is negative the greater of the two is negative.

Considering that factors of 24 are 1, 2,4,6, 12, 24 you have the following options:

-24 and 1. Sum gets to -23. Nope.

-12 and 2. Sum is indeed -10. Check!

-6 and 4. Sum is -2. Nope again.

The two numbers are thus -12 and 2. The factorization becomes

`x^2-10x-24 = (x+2)(x-12)`