$a)x^4+1=x^4+2x^2+1-2x^2={\left(x^2+1\right)}^2-2x^2=$

$={\left(x^2+1\right)}^2-{\left(\sqrt{2}x\right)}^2=\left(x^2+1-\sqrt{2}x\right)\left(x^2+1+\sqrt{2}x\right)=$

$=\left(x^2-\sqrt{2}x+1\right)\left(x^2+\sqrt{2}x+1\right)$