If x+y and y+3x are two factors of the expression x^3- x^2y+xy^2+y^3 then the third factor is

JEE Advanced Mathematics question

If and are two factors of the expression

λ -μ ++

then the third factor is

Answer: (B)

The expression is homogeneous of degree 3 with coefficient of equal to 1, so the third factor is :

+-μ +λ =(y+x)(y+3x)(y+mx)

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Question ID VK-107995