Factorize each of the following polynomials.

x³ – 23x² + 142x – 120

Given,

x³ – 23x² + 142x – 120, put x = 1

then, 1 – 23 × 1 + 142 – 120 = – 143 + 143 = 0

since, this equation is divisible by (x – 1).

according to the question,

x³ – 23x² + 142x – 120 = (x – 1)[x² – 22x + 120]

= (x – 1)[x² – 12x – 10x + 120]

= (x – 1)[x(x – 12) – 10(x – 12)]

= (x – 1)(x – 12)(x – 10).