lean_workbook_plus_69315

Factor $x^4 - 4x^2 - x + 2$ as $x^2(x^2-4)-(x-2) = (x-2)(x^3+2x^2-1) = (x-2)(x+1)(x^2+x+1)$. These factors are irreducible over $\mathbb{Q}$ and $\mathbb{R}$. The third factor has root $a = \frac{-1+i\sqrt{3}}{2} = \zeta_3$ and factors as $(x-a)(x-a^2)$ over $\mathbb{C}$.