a, $x^{4}+3x^{2} + 4 = [(x^{2})^{2}+2.2x^{2}+2^{2}]-x^{2}$
$= (x^{2}+2)^{2} - x^{2}$
$= (x^{2}-x+2)(x^{2}+x+2)$
b,$x^{4}+5x^{2} + 9 = [(x^{2})^{2}+2.3x^{2}+3^{2}]-x^{2}$
$= (x^{2}+3)^{2} - x^{2}$
$= (x^{2}-x+3)(x^{2}+x+3)$
c,$x^{4}-7x^{2} + 1 = [(x^{2})^{2}+2x^{2}+1^{2}]-9x^{2}$
$= (x^{2}+1)^{2} - (3x)^{2}$
$= (x^{2}-3x+1)(x^{2}+3x+1)$
d,$x^{4}-3x^{2} + 9 = [(x^{2})^{2}+2.3x^{2}+3^{2}]-9x^{2}$
$= (x^{2}+3)^{2} - (3x)^{2}$
$= (x^{2}-3x+3)(x^{2}+3x+3)$
