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

Oct 20, 2015

$\left(x + 8\right) \left(x - 3\right)$

#### 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:
$\left(x - 3\right) \left(x + 8\right)$

Hope this helped!

Oct 20, 2015

${x}^{2} + 5 x - 24 = \left(x - 3\right) \left(x + 8\right)$
We need to look at factors of $\left(- 24\right)$:
$\textcolor{w h i t e}{\text{XXX}} \left(- 1 , 24\right) , \left(- 2 , 12\right) , \left(- 3 , 8\right) , \left(- 4 , 6\right) , \left(- 6 , 4\right) , \left(- 8 , 3\right) , \left(- 12 , 2\right) , \left(- 24 , 1\right)$
whose sum is $\left(+ 5\right)$
The only pair satisfying this condition is $\left(- 3 , 8\right)$