# How do you factor the expression x^2 - 13x + 40?

Dec 12, 2015

$\left(x - 5\right) \left(x - 8\right)$

#### Explanation:

There are many ways to factor. One method I like to use is the diamond method when you try to find the two numbers that add up to b and multiply to ac.
$y = a {x}^{2} + b x + c$

So you want to find two numbers that add up to -13 and multiply to 40. You can find the factors of 40 and find the pair that adds up to -13. -8 and -5 multiply to 40 and add up to -13.

$\left(x - 5\right) \left(x - 8\right) = {x}^{2} - 13 x + 40$

You can use foil to test it

${x}^{2} + \left(- 8 x\right) + \left(- 5 x\right) + 40 = {x}^{2} - 13 x + 40$

${x}^{2} - 13 x + 40 = {x}^{2} - 13 x + 40$