\[{x^4} + 2{x^3} + 3{x^2} + 2x - 1 = \left( {{x^2} + x + 1 + \sqrt 2 } \right) \cdot \left( {{x^2} + x + 1 - \sqrt 2 } \right)\]

\[\begin{array}{l} {x_{1,2}} = - \frac{1}{2} \pm \frac{{\sqrt { - 3 + 4\sqrt 2 } }}{2}; \hfill \\ {x_{3,4}} = - \frac{1}{2} \pm i \cdot \frac{{\sqrt {3 + 4\sqrt 2 } }}{2} \hfill \\ \end{array}\]