Question

The HCF of two polynomials \(4x^2(x^2 - 3x + 2)\) and \(12x(x - 2)(x^2 - 4)\) is 4x(x - 2). The LCM of the two polynomials is : 

(a) 12x (x² - 4)

(b) 12x² (x² - 3x + 4)(x² - 2)

(c) 12x² (x² - 3x + 2)(x² - 4)

(d) 12x(x² - 3x - 2)(x² - 4)

Answer 1

(c) 12x²(x² - 3x +2)(x² - 4)

LCM = \(\frac{\text{product of the polynomials}}{HCF}\)

= \(\frac{4x^2(x^2-3x+2)\times12x(x-2)(x^2-4)}{4x(x-2)}\)

= \(\frac{4x^2(x-2)(x-1)\times12x(x-2)(x-2)(x+2)}{4x(x-2)}\)

= 12x²(x - 1)(x - 2)(x - 2)(x + 2)

= 12x²(x² - 3x +2)(x² - 4)