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Null Matrix

If ω is cub...

Question

If $ω$ is cube root of unity the linear factors of $x^{3} + y^{3}$ in complex number is

(x - y) (x - ω y) (x - ω^{2} y)

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(x - y) (x + ω y) (x + ω^{2} y)

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(x + y) (x + ω y) (x + ω^{2} y)

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(x + y) (x - ω y) (x - ω^{2} y)

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Solution

The correct option is D $(x + y) (x + ω y) (x + ω^{2} y)$
$x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})$
$= (x + y) (x^{2} + (ω + ω^{2}) x y + y^{2})$
$= (x + y) (x + ω y) (x + ω^{2} y)$

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