Factors of $x^{4} - x^{2} - 12$ are

(x + 3), (x - 3), (x^{2} + 2)

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(x + 2), (x - 2), (x^{2} - 3)

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(x + 2), (x - 2), (x^{2} + 3)

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(x^{2} + 2), (x^{2} - 6)

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Solution

The correct option is C $(x + 2), (x - 2), (x^{2} + 3)$
We have,

$x^{4} - x^{2} - 12$

$= x^{4} - (4 - 3) x^{2} - 12$

$= x^{4} - 4 x^{2} + 3 x^{2} - 12$

$= x^{2} (x^{2} - 4) + 3 (x^{2} - 4)$

$= (x^{2} - 4) (x^{2} + 3)$

$= (x^{2} - 2^{2}) (x^{2} + 3)$

$= (x + 2) (x - 2) (x^{2} + 3)$
Hence, this is the answer.

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