2015 · Q37
The HCF and LCM of two polynomials are (x + y) and (3x^5+5x^4y+2x³y²-3x²y³-5xy^4-2y^5) respectively. If one of the polynomials is (x² - y²), then the other polynomial is
Elementary MathematicsHCF and LCM
- A3x^4-8x³y+10x²y²+7xy³-2y^4
- B3x^4-8x³y-10x²y²+7xy³+2y^4
- C3x^4+8x³y+10x²y²+7xy³+2y^4
- D3x^4+8x³y-10x²y²+7xy³+2y^4
Explanation
The other polynomial = HCF × LCM ÷ (x²−y²) = LCM ÷ (x−y). Dividing 3x⁵+5x⁴y+2x³y²−3x²y³−5xy⁴−2y⁵ by (x−y) gives 3x⁴+8x³y+10x²y²+7xy³+2y⁴ with zero remainder (option C), verified by symbolic polynomial division.