a^4+3 a^2+4 =a^4+4 a^2-a^2+4 = (a^4+4 a^2+4 )-a^2 = [ (a^2 )^2+2 a^2 2+2^2 ]-a^2 = (a^2+2 )^2-a^2 = [ (a^2+2 )-a ] [ (a^2+2 )+a ] = (a^2-a+2 ) (a^2+a+2 )

Solve: a^4+3 a^2+4

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Solve:
$a^4+3 a^2+4$

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Answer

$a^4+3 a^2+4$
$=a^4+4 a^2-a^2+4$
$=\left(a^4+4 a^2+4\right)-a^2$
$=\left[\left(a^2\right)^2+2 \times a^2 \times 2+2^2\right]-a^2$
$=\left(a^2+2\right)^2-a^2$
$=\left[\left(a^2+2\right)-a\right]\left[\left(a^2+2\right)+a\right]$
$=\left(a^2-a+2\right)\left(a^2+a+2\right)$

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