The LCM and HCF of two polynomials p(x) and q(x) are (x + a)(x^3 - a^3) and (x^2 - ax + a^2), respectively. If p(x) = x^4 + a^2x^2 + a^4, then what is q(x) equal to ?
- A. x^4 - 2a^2x^2 + a^4
- B. x^4 + 2a^2x^2 + a^4
- C. x^2 - a^2 ✓
- D. x^4 - a^2x^2 + a^4
Correct Answer: C. x^2 - a^2
Explanation
Using the relation p(x) \times q(x) = \text{LCM} \times \text{HCF}, we divide the product of the LCM and HCF by p(x). Simplifying (x^2-a^2)(x^4+a^2x^2+a^4) / (x^4+a^2x^2+a^4) results in x^2-a^2.
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