x^2 - 5x - 24 how can i factor this out?

Answer 1

x^2 - 5x - 24 = (x + 3) * (x - 8)

Answer 2

There are two ways.

One way is to memorize the quadratic formula, and plug in the coefficients. That works for any quadratic equation.

The second way is to actually factor the coefficients. This problem is pretty easy because the "a" coefficient is 1.

If the "c" coefficient is positive, you look for a sum of factors that add up to "b." If the "c" coefficient is negative you look for a difference of factors that add up to "b."

In this problem the "c" coefficient is negative (-24), so you need to find the factors of "|c|" (24) which have a difference of "b" (-5). The factors of |c| are (1, 24) (2, 12) (3, 8) and (4, 6). Looking through the list you see that (3, 8) has a span of 5, so to get -5 your factors need to be -8 and +3 (-8 + 3 = -5). This gives you the factors (x-8) (x+3).

After a while you get a feel for it, and can do simple ones like this in your head.

If there is an "a" coefficient other than 1 or -1 (such as 12x^2, or -7x^2), the problem is harder because you have to factor "a" as well as "c" and find cross products of factors of "a" and "c" that add up to or have a difference of "b."

At this point it's usually easier to use the quadratic formula to find the roots.

Answer 3

x^2 - 5x - 24
= x^2 - 8x + 3x - 24
= x*(x-8) + 3*(x-8)
= (x+3)*(x-8) ...final Answer

Answer 4

x^2 - 5x - 24
= x^2 - 8x + 3x - 24
= x*(x-8) + 3*(x-8)
= (x+3)*(x-8) ...

Answer 5

(x - 8).(x + 3)