Решите уравнение x^3-2x^2-9x+18=0.

Ответ:

\[x^{3} - 2x^{2} - 9x + 18 = 0\]

\[x^{2}(x - 2) - 9 \cdot (x - 2) = 0\]

\[(x - 2)\left( x^{2} - 9 \right) = 0\]

\[(x - 2)(x - 3)(x + 3) = 0\]

\[x - 2 = 0;\ \ \ \ \ x + 3 = 0;\ \ \ \ \ x - 3 = 0\]

\[x = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 3\ \ \ \ \ \ \ \ \ \ \ \ x = 3\]

\[Ответ:x = \pm 3;\ \ x = 2.\]