Factorize each of the following polynomials.

2x³ – 9x² + 7x + 6

Given,

2x³ – 9x² + 7x + 6,

put x = 2

Then, 16 – 36 + 14 + 6 = 0

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

according to the question,

2x³ – 9x² + 7x + 6 = (x – 2)(2x² – 5x – 3)

= (x – 2)[2x² – 6x + x – 3]

= (x – 2)[2x(x – 3) + 1(x – 3)]

= (x – 2)(x – 3)(2x + 1)