Разложить многочлен на множители x^4-2*x^3-11*x^2-10*x-29

Комбинаторика

       4       2             3
-29 + x  - 11*x  - 10*x - 2*x 

$$x^{4} - 2 x^{3} - 11 x^{2} - 10 x - 29$$

Разложение на множители

/                                                                                                             ___________________________________________________________________________________________________________________________________________________________\ /                                                                                                             ___________________________________________________________________________________________________________________________________________________________\ /                         ___________________________________________________________________________________________________________________________________________________________                                                                                    \ /                                                                                                             ___________________________________________________________________________________________________________________________________________________________\
|                                                                                                            /             _______________________                                                                                                                       | |                                                                                                            /                                                                                                 _______________________                                   | |                        /                                                                                                 _______________________                                                                                                                       | |                                                                                                            /             _______________________                                                                                                                       |
|                                                                                                           /             /             _________                                                                                                                        | |                                                                                                           /                                                                                                 /             _________                                    | |                       /                                                                                                 /             _________                                                                                                                        | |                                                                                                           /             /             _________                                                                                                                        |
|                                                                                                          /   50        /    12041   \/ 1171011                                             44                                                        287               | |                                                                                                          /   50                                           44                                               /    12041   \/ 1171011                   287               | |                      /   50                                           44                                               /    12041   \/ 1171011                   287                                                                                                   | |                                                                                                          /   50        /    12041   \/ 1171011                                             44                                                        287               |
|                                                                                                         /    -- - 2*3 /   - ----- + -----------  + --------------------------------------------------------------------------------- + ------------------------------- | |                                                                                                         /    -- - --------------------------------------------------------------------------------- - 2*3 /   - ----- + -----------  + ------------------------------- | |                     /    -- - --------------------------------------------------------------------------------- - 2*3 /   - ----- + -----------  + -------------------------------                                                                                     | |                                                                                                         /    -- - 2*3 /   - ----- + -----------  + --------------------------------------------------------------------------------- + ------------------------------- |
|                    _______________________________________________________________________             /     3      \/       216         18                  _______________________________________________________________________           _______________________ | |                    _______________________________________________________________________             /     3              _______________________________________________________________________     \/       216         18                _______________________ | |                    /     3              _______________________________________________________________________     \/       216         18                _______________________              _______________________________________________________________________| |                    _______________________________________________________________________             /     3      \/       216         18                  _______________________________________________________________________           _______________________ |
|                   /             _______________________                                               /                                                     /             _______________________                                             /             _________  | |                   /             _______________________                                               /                    /             _______________________                                                                              /             _________  | |                   /                    /             _______________________                                                                              /             _________              /             _______________________                                   | |                   /             _______________________                                               /                                                     /             _______________________                                             /             _________  |
|                  /             /             _________                                               /                                                     /             /             _________                                             /    12041   \/ 1171011   | |                  /             /             _________                                               /                    /             /             _________                                                                              /    12041   \/ 1171011   | |                  /                    /             /             _________                                                                              /    12041   \/ 1171011              /             /             _________                                    | |                  /             /             _________                                               /                                                     /             /             _________                                             /    12041   \/ 1171011   |
|                 /   25        /    12041   \/ 1171011                   287                         /                                                     /   25        /    12041   \/ 1171011                   287                  18*3 /   - ----- + -----------  | |                 /   25        /    12041   \/ 1171011                   287                         /                    /   25        /    12041   \/ 1171011                   287                                                   18*3 /   - ----- + -----------  | |                 /                    /   25        /    12041   \/ 1171011                   287                                                   18*3 /   - ----- + -----------            /   25        /    12041   \/ 1171011                   287               | |                 /   25        /    12041   \/ 1171011                   287                         /                                                     /   25        /    12041   \/ 1171011                   287                  18*3 /   - ----- + -----------  |
|                /    -- + 2*3 /   - ----- + -----------  - -------------------------------          /                                                     /    -- + 2*3 /   - ----- + -----------  - -------------------------------       \/       216         18      | |                /    -- + 2*3 /   - ----- + -----------  - -------------------------------          /                    /    -- + 2*3 /   - ----- + -----------  - -------------------------------                                        \/       216         18      | |                /                    /    -- + 2*3 /   - ----- + -----------  - -------------------------------                                        \/       216         18               /    -- + 2*3 /   - ----- + -----------  - ------------------------------- | |                /    -- + 2*3 /   - ----- + -----------  - -------------------------------          /                                                     /    -- + 2*3 /   - ----- + -----------  - -------------------------------       \/       216         18      |
|               /     3      \/       216         18                _______________________         /                                                     /     3      \/       216         18                _______________________                                    | |               /     3      \/       216         18                _______________________         /                    /     3      \/       216         18                _______________________                                                                     | |               /                    /     3      \/       216         18                _______________________                                                                             /     3      \/       216         18                _______________________ | |               /     3      \/       216         18                _______________________         /                                                     /     3      \/       216         18                _______________________                                    |
|              /                                                   /             _________         /                                                     /                                                   /             _________                                     | |              /                                                   /             _________         /                    /                                                   /             _________                                                                      | |              /                    /                                                   /             _________                                                                             /                                                   /             _________  | |              /                                                   /             _________         /                                                     /                                                   /             _________                                     |
|             /                                                   /    12041   \/ 1171011         /                                                     /                                                   /    12041   \/ 1171011                                      | |             /                                                   /    12041   \/ 1171011         /                    /                                                   /    12041   \/ 1171011                                                                       | |             /                    /                                                   /    12041   \/ 1171011                                                                             /                                                   /    12041   \/ 1171011   | |             /                                                   /    12041   \/ 1171011         /                                                     /                                                   /    12041   \/ 1171011                                      |
|            /                                              18*3 /   - ----- + -----------       /                                                     /                                              18*3 /   - ----- + -----------                                     | |            /                                              18*3 /   - ----- + -----------       /                    /                                              18*3 /   - ----- + -----------                                                                      | |            /                    /                                              18*3 /   - ----- + -----------                                                                           /                                              18*3 /   - ----- + -----------  | |            /                                              18*3 /   - ----- + -----------       /                                                     /                                              18*3 /   - ----- + -----------                                     |
|      1   \/                                                  \/       216         18         \/                                                    \/                                                  \/       216         18                                         | |      1   \/                                                  \/       216         18         \/                   \/                                                  \/       216         18                                                                          | |      1   \/                   \/                                                  \/       216         18                                                                             \/                                                  \/       216         18      | |      1   \/                                                  \/       216         18         \/                                                    \/                                                  \/       216         18                                         |
|x + - - - --------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|x + - - + --------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|x + - - - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------|*|x + - - - --------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
\      2                                           2                                                                                                                               2                                                                                     / \      2                                           2                                                                                                                               2                                                                                     / \      2                                                                                       2                                                                                                                                2                                        / \      2                                           2                                                                                                                               2                                                                                     /

$$\left(x + \left(- \frac{1}{2} + \frac{\sqrt{- \frac{287}{18 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}}} + 2 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}} + \frac{25}{3}}}{2} + \frac{\sqrt{- \frac{44}{\sqrt{- \frac{287}{18 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}}} + 2 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}} + \frac{25}{3}}} - 2 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}} + \frac{287}{18 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}}} + \frac{50}{3}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}} + \frac{287}{18 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}}} + \frac{50}{3} + \frac{44}{\sqrt{- \frac{287}{18 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}}} + 2 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}} + \frac{25}{3}}}}}{2} - \frac{\sqrt{- \frac{287}{18 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}}} + 2 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}} + \frac{25}{3}}}{2} - \frac{1}{2}\right)\right) \left(x + \left(- \frac{1}{2} + \frac{\sqrt{- \frac{287}{18 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}}} + 2 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}} + \frac{25}{3}}}{2} - \frac{\sqrt{- \frac{44}{\sqrt{- \frac{287}{18 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}}} + 2 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}} + \frac{25}{3}}} - 2 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}} + \frac{287}{18 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}}} + \frac{50}{3}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{- \frac{287}{18 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}}} + 2 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}} + \frac{25}{3}}}{2} - \frac{1}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}} + \frac{287}{18 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}}} + \frac{50}{3} + \frac{44}{\sqrt{- \frac{287}{18 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}}} + 2 \sqrt[3]{- \frac{12041}{216} + \frac{\sqrt{1171011}}{18}} + \frac{25}{3}}}}}{2}\right)\right)$$

Объединение рациональных выражений

-29 + x*(-10 + x*(-11 + x*(-2 + x)))

$$x \left(x \left(x \left(x - 2\right) - 11\right) - 10\right) - 29$$