One of the factors of $x^4+x^2+1$ is

add and subtract ‘$x^2$ ’

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

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

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

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

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