Factor the expression. x2 - 51x + 144

x^2 - 51x + 144

What times what makes 144?

12 * 12

9 * 16

and so on

but what do they add up to?

12 * 12 = 144, 12 + 12 = 24

9 * 16 = 144, 9 + 16 = 25

8 * 18 = 144, 8 + 18 = 26

6 * 24 = 144, 6 + 24 = 30

4 * 36 = 144, 4 + 36 = 40

3 * 48 = 144, 3 + 48 = 51

There's our middle term, the 51.

If we did (x+3)(x+48) then the middle term would be +51, but we want -51, so it's this:

(x-3)(x-48) = x^2 -51x + 144