Question

Factor the expression x2 − 5x − 24.

Answer 1

x^2 + 3x - 8x - 24
= (x + 3)(x - 8)
First you should find two numbers whose sum is -5 and product is -24(in this case 3 and -8).
Then you should split the middle term like I have done here.
Group the terms and factor - there you have the factored expression!!

Answer 2

do the coefficient of x² multiplied by the constant
1x-24=-24

what two numbers multiply to give -24 but add to give -5?

list factors of -24

1 24
2 12
3 8
4 6
-1 24
-2 12
-3 8
-4 6
1 -24
2 -12
3 -8
4 -6

3+-8=-5

use that

you now have
(x + 3 ) (x - 8)