In order to factorize the given expression, we find to find two numbers p and q such that:

p + q = -22, pq = 120

Clearly,

-12 – 10 = -22, (-12) (-10) = -120

Therefore, split -22x as -12x – 10x

Therefore,

x² - 22x + 120 = x² - 12x – 10x + 120

= x (x - 12) – 10 (x - 12)

= (x – 10) (x - 12)