Factorize each of the following polynomials.

x³ – 5x² – 2x + 24

Given,

x³ – 5x² – 2x + 24,put x = – 2

then, – 8 – 20 + 4 + 24 = 0

since, this equation is divisible by (x + 2).

according to the question,

x³ – 5x² – 2x + 24 = (x + 2)(x² – 7x + 12)

= (x + 2)[x² – 4x – 3x + 12]

= (x + 2)[x(x – 4) – 3(x – 4)]

= (x + 2)(x – 4)(x – 3)