Factor the expressions.

x2 + 22x + 120 =

(x + 10 and (x + 12)

Step-by-step explanation:

x^2 + 22x + 120 = (?) (?)

We need to find two constants whose product is 120 and whose sum is 22.

Let the two constants be a and b. Then:

a*b = 120 and a + b = 22.

It's a bit easier to find a and b such that a + b = 22: 2 and 20, 4 and 18, 6 and 16, and so on. Note that 6 + 16 = 22 (correct) but that 6*16 = 96 (not correct). Try 8 and 14, 10 and 12. Note that 10 + 12 = 22 and that 10*12 = 120. So the desired roots are {10, 12} and the desired factors are (x + 10 and (x + 12).

Check: Does (x + 10) (x + 12) work out to x^2 + 22x + 120?

x^2 + 12x + 10x + 120 = x^2 + 22x + 120? YES

The factors are (x + 10 and (x + 12).