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Factor of a Polynomial

Factors of ...

Question

Factors of $x^{4} + 5 x^{2} + 9$ are:

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

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

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

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

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Solution

The correct option is D $(x^{2} - x + 3) (x^{2} + x + 3)$
$x^{4} + 5 x^{2} + 9$
$= x^{4} + 6 x^{2} + 9 - x^{2}$
$= {(x^{2} + 3)}^{2} - x^{2}$
$= (x^{2} - x + 3) (x^{2} + x + 3)$ ..... $∵ x^{2} - y^{2} = (x + y) (x - y)$

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