Answer
(a) $(x^{2} + 2)(x+1)(x-1)$
(b) $(x^2+2x+3)(x^2-2x+3)$
(c) $(x^2+2x+4)(x^2-2x+4)$
(d) $(x^2+1)^2$
Work Step by Step
(a) $x^{4} + x^{2} - 2$
$= (x^{2}+2)(x^{2}-1)$
$= (x^{2}+2)(x+1)(x-1)$
(b) $x^4$+$2x^2+9$
= $x^4$+$6x^2$-$4x^2+9$
=$(x^2+3)^2$-$(2x)^2$
=($x^2+2x+3)(x^2-2x+3)$
(c) $x^4+4x^2+16$
=$(x^2)^2$+$(4)^2$+2($x^2$)(4)-2($x^2$)(4)+4($x^2$)
=$(x^2+4)^2-8x^2+4x^2$
=$(x^2+4)^2-4x^2$
=$(x^2+4)^2-(2x)^2$
=$(x^2+2x+4)(x^2-2x+4)$
(d) $x^4+2x^2+1$
$=x^4+2(x^2)(1)+1^2$
$=(x^2+1)^2$
