Factorise: $a^{4} + 5 a^{2} + 9$

(a^{2} + a + 3) (a^{2} - a + 3)

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(a^{2} + a - 3) (a^{2} - a + 3)

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(a^{2} - a - 3) (a^{2} + a + 3)

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None of these

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Solution

The correct option is A $(a^{2} + a + 3) (a^{2} - a + 3)$
$a^{4} + 5 a^{2} + 9$
$= (a^{2})^{2} + 2 a^{2} (3) + (3)^{2} - a^{2}$
$= (a^{2} + 3)^{2} - a^{2}$
$= (a^{2} + 3 + a) (a^{2} + 3 - a)$

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