\[\boxed{\text{355\ (355).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ x^{3} + 2x^{2} + 3x + 2 = 0\]
\[x_{1} = - 1 \Longrightarrow корень\ уравнения.\]
\[(x + 1)\left( x^{2} + x + 2 \right) = 0.\]
\[\ x^{2} + x + 2 = 0\]
\[D = 1 - 4 \cdot 2 < 0 \Longrightarrow корней\ нет.\]
\[Ответ:x = - 1.\]
\[\textbf{б)}\ x^{3} + 4x^{2} - 3x - 6 = 0\]
\[x_{1} = - 1 \Longrightarrow корень.\]
\[(x + 1)\left( x^{2} + 3x - 6 \right) = 0\]
\[x^{2} + 3x - 6 = 0\]
\[D = 9 + 4 \cdot 6 = 33\]
\[x_{1,2} = \frac{- 3 \pm \sqrt{33}}{2}.\]
\[Ответ:x = - 1;\ x = \frac{- 3 - \sqrt{33}}{2};\]
\[\ x = \frac{- 3 + \sqrt{33}}{2}.\]