Factorize each of the following polynomials.

2x³ + 11x² – 7x – 6

Given,

2x³ + 11x² – 7x – 6,

put x = 1

Then, 2 + 11 – 7 – 6 = 0

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

according to the question,

2x³ + 11x² – 7x – 6 = (x – 1)(2x² + 13x + 6)

= (x – 1)[2x² + 12x + x + 6]

= (x – 1)[2x(x + 6) + 1(x + 6)]

= (x – 1)(2x + 1)(x + 6)