Question

Factorize each of the following algebraic expressions:

40 + 3x - x²

Answer 1

- (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)