2022 · Q26
Let p(x) = x⁴ + x² +1, q(x) = x⁴ - 2x³ + 3x² - 2x + 1. If GCD of p(x) and q(x) is x² - x + 1, then what is their LCM?
Elementary MathematicsHCF and LCM
- A(x² + x + 1)(x² - x + 1)²
- B(x⁴ + x² + 1)² (x² - x + 1)
- C(x⁴ + x² + 1)(x² + x + 1)²
- D(x⁴ + x² + 1)(x² - x + 1)²
Explanation
p(x) = (x²+x+1)(x²−x+1) and q(x) = (x²−x+1)² (expand to verify). With GCD = x²−x+1, LCM = p·q/GCD = (x²+x+1)(x²−x+1)². The keyed option is A.