Question

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

• A. \( 4x(x - 2) \)
• B. \( 12x^2 (x^2 - 3x + 2) (x^2 + 4) \)
• C. \( x^2(x^2 - 3x + 2)(x^2 - 4) \)
• D. \( 12x^2 (x^2 - 3x + 2) (x^2 - 4) \)

Hint:

To find the LCM of polynomials, multiply the polynomials and divide by the HCF to avoid repeated factors.

Answer 1

The Correct Option is D

To find the LCM of two polynomials, we use the formula: \[ \text{LCM} = \frac{p(x) \times q(x)}{\text{HCF}(p(x), q(x))} \] Here, we are given that \( \text{HCF}(p(x), q(x)) = 4x(x - 2) \). The LCM is: \[ \text{LCM}(p(x), q(x)) = \frac{4x^2(x^2 - 3x + 2) \times 12x(x - 2)(x^2 - 4)}{4x(x - 2)} = 12x^2(x^2 - 3x + 2)(x^2 - 4) \] Thus, the correct answer is \( 12x^2(x^2 - 3x + 2)(x^2 - 4) \).