Find G.C.D of: $8 (x^{4} - 16)$ and $12 (x^{3} - 8)$

4 (x - 2)

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3 (x^{3} - 8)

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2 (x^{2} - 4)

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None of these

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Solution

The correct option is A $4 (x - 2)$
$p (x) = 8 (x^{4} - 16)$
$= 4 \times 2 [(x^{2})^{2} - 4^{2}]$
$= 4 \times 2 (x^{2} - 4) (x^{2} + 4)$
$= 4 \times 2 (x + 2) (x - 2) (x^{2} + 4)$
and
$q (x) = 12 (x^{3} - 8)$
$= 4 \times 3 (x^{3} - 2^{3})$
$= 4 \times 3 (x - 2) (x^{2} + 2 x + 4)$
$∴$ G.C.D of $p (x)$ and $q (x) = 4 (x - 2)$
Option A is correct.

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