2020 · Q31
What is the HCF of the polynomials x⁶ − 3x⁴ + 3x² − 1 and x³ + 3x² + 3x + 1?
Elementary MathematicsHCF and LCM
- A(x + 1)
- B(x + 1)²
- Cx³ + 1
- D(x + 1)³
Explanation
x^6-3x^4+3x^2-1 = (x^2-1)^3 = (x-1)^3(x+1)^3, and x^3+3x^2+3x+1 = (x+1)^3. Their HCF is (x+1)^3 - option (D). Indeed (x+1)^3 divides both polynomials, and no higher power of (x+1) divides the first one.