2026 · Q18
What is the HCF of x³ + x²y − 10xy² + 8y³ and x³ + x²y − 4xy² − 4y³?
Elementary MathematicsHCF and LCM
- A(x−y)
- B(x−2y)
- C(x+2y)
- D(x+4y)
Explanation
Setting y = 1, the first polynomial becomes x³ + x² − 10x + 8, which factors as (x − 2)(x − 1)(x + 4) since x = 2, 1 are roots. The second becomes x³ + x² − 4x − 4 = x²(x + 1) − 4(x + 1) = (x + 1)(x − 2)(x + 2). The only common linear factor is (x − 2), which in two variables is (x − 2y), option B.