Решите уравнение: x^3+4x^2+5x+2=0.

\[x^{3} + 4x^{2} + 5x + 2 = 0\]

\[\left( x^{3} + x^{2} \right) + \left( 3x^{2} + 3x \right) + (2x + 2) = 0\]

\[x^{2}(x + 1) + 3x(x + 1) + 2(x + 1) = 0\]

\[(x + 1)\left( x^{2} + 3x + 2 \right) = 0\]

\[1)\ x + 1 = 0\]

\[x = - 1.\]

\[2)\ x^{2} + 3x + 2 = 0\]

\[x_{1} + x_{2} = - 3;\ \ x_{1} \cdot x_{2} = 2\]

\[x_{1} = - 2;x_{2} = - 1.\]

\[Ответ:x = - 1;x = - 2.\]