Factorize each of the following algebraic expressions:

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

p + q = -11, pq = -42

Clearly,

3 – 14 = -11, 3 (-14) = -42

Therefore, split (-11x) as 3x – 14x

Therefore,

x² - 11x – 42 = x² + 3x – 14x – 42

= x (x + 3) – 14 (x + 3)

= (x – 14) (x + 3)