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Multiple Choice Questions

The HCF and LCM of two polynomials are x y and 3x5 5x4y 2x3y2 3x2y3 5xy4 2y5 respectively If one of ...........

Quantitative Aptitude (CDS) LCM, HCF

The HCF and LCM of two polynomials are (x + y) and (3x⁵ + 5x⁴y + 2x³y² - 3x²y³ - 5xy⁴ - 2y⁵) respectively. If one of the polynomials is (x² - y²), then the other polynomial is

3x⁴ - 8x³y + 10x²y² + 7xy³ - 2y⁴

3x⁴ - 8x³y - 10x²y² + 7xy³ + 2y⁴

3x⁴ + 8x³y + 10x²y² + 7xy³ + 2y⁴

3x⁴ + 8x³y - 10x²y² + 7xy³ + 2y⁴

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Explanation:

3x⁵+5x⁴y+2x³y²−3x²y³−5xy⁴−2y⁵
=3x⁵−3x²y³+5x⁴y−5xy⁴+2x³y²−2y⁵
=3x²(x³−y³)+5xy(x³−y³)+2y²(x³−y³)

=(x³−y³)(3x²+5xy+2y²)

=(x−y)(x²+xy+y²)(3x²+5xy+2y²)

Remember:
Product of two polynomials = Product of HCF and LCM of two polynomials.
Therefore,other polynomial
(x+y)×(x−y)(x²+xy+y²)
=(3x²+5xy+2y²)/x²−y²
=(x²+xy+y²)(3x²+5xy+2y²)

=3x⁴+8x³y+10x²y²+7xy³+2y⁴