Question

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

Answer 1

`(x-5)(x-8)`

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=ax^2+bx+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.

`(x-5)(x-8)=x^2-13x+40`

You can use foil to test it

`x^2+(-8x)+(-5x)+40=x^2-13x+40`

`x^2-13x+40=x^2-13x+40`