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:
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:
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To find the LCM of polynomials, multiply the polynomials and divide by the HCF to avoid repeated factors.
Updated On: Apr 25, 2025
- \( 4x(x - 2) \)
- \( 12x^2 (x^2 - 3x + 2) (x^2 + 4) \)
- \( x^2(x^2 - 3x + 2)(x^2 - 4) \)
- \( 12x^2 (x^2 - 3x + 2) (x^2 - 4) \)
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The Correct Option is D
Solution and Explanation
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 \( 12x^2(x^2 - 3x + 2)(x^2 - 4) \).
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