Factors of $x^{6} + 9 x^{3} + 8$ are:

(x - 2) (x^{2} + 2 x + 4)

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(x + 2) (x^{2} - 2 x + 4) (x + 1) (x^{2} - x + 1)

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(x - 1) (x^{2} - 2 x + 4) (x + 1) (x^{2} - x + 1)

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None of these

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Solution

The correct option is B $(x + 2) (x^{2} - 2 x + 4) (x + 1) (x^{2} - x + 1)$ .
$x^{6} + 9 x^{3} + 8 = x^{6} + 8 x^{3} + x^{3} + 8$
$= x^{3} (x^{3} + 8) + 1 (x^{3} + 8)$
$= (x^{3} + 8) (x^{3} + 1)$
$= (x^{3} + 2^{3}) (x^{3} + 1^{3})$
$= (x + 2) (x^{2} - 2 x + 4) (x + 1) (x^{2} - x + 1)$

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