I am having problems factoring the following quartic with quadratic roots.
$$3x^4 + x^3 + 2x^2 - x + 1 = \left(x^2 + x + 1 \right) \left( 3x^2 - 2x + 1 \right)$$
All the ways I've found online till now only show to factor quartics including linear factors. None of them show the process to factor the equation with pure quadratic factors. Could you please suggest a way to do so?