The correct solution should be $$(x^2-x+1)(x^2+x+1)(x^4-x^2+17)$$
This is originally posted as a high school entrance exam question, no calculators allowed.
So this is meant to be doable by hard. However, the solution doesn't have any linear factors, making it hard to find a root.
Is there a method to factorize by hand?
Edit: It is now answered that substituting $z=x^2$ can make it factorizeable. Then, using $$a^4+a^2+1 = (a^2+a+1)(a^2-a+1)$$
Can further factorize it into the correct solution.