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Division Algorithm for a Polynomial

If x + y + z ...

Question

If $x + y + z = 0$
then $x^{3} + y^{3} + z^{3}$ =___?

A

0

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B

-3xyz

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C

3xyz

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D

2xyz

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Solution

The correct option is C
3xyz

We know that, $x^{3}$ + $y^{3}$ + $z^{3} - 3 x y z$ = $(x + y + z) (x^{2} + y^{2} + z^{2} - 2 x y - 2 y z - 2 z x)$

If $x + y + z = 0$ then,
$x^{3} + y^{3} + z^{3} - 3 x y z = (0) (y^{2} + z^{2} - 2 x y - 2 y z - 2 z x) = 0$

$\Rightarrow x^{3} + y^{3} + z^{3} = 3 x y z$

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Similar questions

If $x + y + z = 0$
then $x^{3} + y^{3} + z^{3}$ =___?

If $x + y + z = 0,$
then find the value of $x^{3} + y^{3} + z^{3} .$

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, what can be said about

x^{3} + y^{3} + z^{3}

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Q. If x + y + z = 0, then (x + y)³+ (y + z)³ + (z + x)³ = ________.

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