Question

Factorize each of the following algebraic expressions:

x² + 14x + 45

Answer 1

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

p + q = 14, pq = 45

Clearly,

5 + 9 = 14, 5 (9) = 45

Therefore, split 14x as 5x + 9x

Therefore,

x² + 14x + 45 = x² + 5x + 9x + 45

= x (x + 5) – 9 (x + 5)

= (x + 9) (x + 5)