Factorize :
$x^{4} + 4 x^{2} + 3$

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Solution

$x^{4} + 4 x^{2} + 3$
$= x^{4} + 4 x^{2} + 4 - 1$
$= (x^{4} + 4 x^{2} + 4) - 1$
$= (x^{2} + 2)^{2} - 1^{2}$
$= (x^{2} + 2 + 1) (x^{2} + 2 - 1)$
$= (x^{2} + 3) (x^{2} + 1)$

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