HCF and LCM of two polynomials are x - 2 and x³ + 3x² - 6x - 8 respectively. If one polynomial is x² - x - 2, find the second polynomial?

x² + 2x - 8

x² - 2x - 8

x² - 2x + 8

None of these

HCF = x - 2

LCM = x^3 + 3x^2 - 6x - 8

One polynomial = x^2 - x - 2 = (x - 2)(x + 1)

Factorize LCM:

x^3 + 3x^2 - 6x - 8 = (x - 2)(x^2 + 5x + 4) = (x - 2)(x + 1)(x + 4)

Using HCF × LCM = Product of polynomials:

(x - 2) × (x - 2)(x + 1)(x + 4) = (x - 2)(x + 1) × Second polynomial

Second polynomial = (x - 2)(x + 4) = x^2 + 2x - 8