Question

How do you factor `x^2+5x-24`?

Answer 1

`(x+8)(x-3)`

Explanation:

In order to factor, we need to consider 2 things.
1.) What are the factors of the constant?
2.) Which of those add to equal the coefficient before the x value?

In this particular equation, we have the constant being 24. The first two factors that come to mind are 6 and 4, and 8 and 3. Since it is -24, we need one of these numbers to be negative.

Let's look at our "b" value, or the coefficient behind the x value, 5. Looking at our factors and thinking of addition (since one of them must be negative, it will most likely be subtraction instead of addition) I can see that `8 + -3 = 5`, which is one of the factors of -24.

This means that we can factor our equation using these numbers, getting us the following:
`(x - 3)(x+8)`

Hope this helped!

Answer 2

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

Explanation:

We need to look at factors of `(-24)`:
`color(white)("XXX")(-1,24), (-2,12), (-3,8), (-4,6), (-6,4), (-8,3), (-12,2), (-24,1)`
whose sum is `(+5)`

The only pair satisfying this condition is `(-3,8)`