Find G.C.D of: $(x^{2} - 9) (x - 3)$ and $x^{2} + 6 x + 9$

(x + 3)^{2}

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(x-3)

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(x+3)

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None of these

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Solution

The correct option is C (x+3)
$p (x) = (x^{2} - 9) (x - 3)$
$= (x^{2} - 3^{2}) (x - 3)$
$= (x - 3) (x + 3) (x - 3)$
and
$q (x) = x^{2} + 6 x + 9$
$= x^{2} + 3 x + 3 x + 9$
$= x (x + 3) + 3 (x + 3)$
$= (x + 3) (x + 3)$
$∴$ G.C.D of $p (x)$ and $q (x) = x + 3$
Option C is correct.

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