What is the HCF of the polynomials x^{6}-3x^{4}+3x^{2}-1 and x^{3}+3x^{2}+3x+1?
- A. x+1
- B. (x+1)^{2}
- C. x^{2}+1
- D. (x+1)^{3} ✓
Correct Answer: D. (x+1)^{3}
Explanation
Factoring both polynomials: x^6-3x^4+3x^2-1 = (x^2-1)^3 = (x-1)^3(x+1)^3. The second polynomial is x^3+3x^2+3x+1 = (x+1)^3. The highest common factor is (x+1)^3.
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