Question

If $\omega$ is cube root of unity the linear factors of $x^3 + y^3$ in complex number is

• A. $(x -y) (x - \omega y)(x -\omega^2 y)$
• B. $(x -y) (x + \omega y)(x +\omega^2 y)$
• C. $(x + y) (x + \omega y)(x +\omega^2 y)$
• D. $(x + y) (x - \omega y)(x - \omega^2 y)$

Answer 1

Answer: (C)

$x^3 + y^3 = (x + y) (x^2 - xy + y^2)$
$= (x + y) (x^2 + (\omega + \omega^2) xy + y^2)$
$= (x + y) (x + \omega y) (x + \omega^2y)$