Factorize each of the following algebraic expressions:

- (x² – 3x – 40)

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

p + q = - 3, pq = - 40

Clearly,

5 – 8 = -3, 5 (-8) = -40

Therefore, split -3x as 5x – 8x

Therefore,

x² - 3x – 40 = x² + 5x – 8x – 40

= x (x + 5) – 8 (x + 5)

= (x – 8) (x + 5)