Разложить многочлен на множители x^5/5-x^4/4-x^2-4*x

Объединение рациональных выражений

  /        /       2           \\
x*\-80 + x*\-20 + x *(-5 + 4*x)//
---------------------------------
                20               

$$\frac{x \left(x \left(x^{2} \left(4 x - 5\right) - 20\right) - 80\right)}{20}$$

Разложение на множители

  /                                                                                                       _________________________________________________________________________________________________________________________________________________\ /                          _________________________________________________________________________________________________________________________________________________                                                                             \ /                                                                                                       _________________________________________________________________________________________________________________________________________________\ /                                                                                                       _________________________________________________________________________________________________________________________________________________\
  |                                                                                                      /             ____________________                                                                                                                | |                         /             ____________________                                                                                                                                                                                             | |                                                                                                      /             ____________________                                                                                                                | |                                                                                                      /             ____________________                                                                                                                |
  |                                                                                                     /             /            _______                                                                                                                 | |                        /             /            _______                                                                                                                                                                                              | |                                                                                                     /             /            _______                                                                                                                 | |                                                                                                     /             /            _______                                                                                                                 |
  |                                                                                                    /   25        /    25   5*\/ 15215                                          2685                                                    115             | |                       /   25        /    25   5*\/ 15215                                          2685                                                    115                                                                                          | |                                                                                                    /   25        /    25   5*\/ 15215                 115                                                    2685                                      | |                                                                                                    /   25        /    25   5*\/ 15215                 115                                                    2685                                      |
  |                                                                                                   /    -- - 2*3 /   - -- + -----------  - ------------------------------------------------------------------------------ + --------------------------- | |                      /    -- - 2*3 /   - -- + -----------  - ------------------------------------------------------------------------------ + ---------------------------                                                                              | |                                                                                                   /    -- - 2*3 /   - -- + -----------  + --------------------------- + ------------------------------------------------------------------------------ | |                                                                                                   /    -- - 2*3 /   - -- + -----------  + --------------------------- + ------------------------------------------------------------------------------ |
  |                     ________________________________________________________________             /     32     \/      64        32                      ________________________________________________________________          ____________________ | |                     /     32     \/      64        32                      ________________________________________________________________          ____________________              ________________________________________________________________| |                     ________________________________________________________________             /     32     \/      64        32               ____________________                 ________________________________________________________________ | |                     ________________________________________________________________             /     32     \/      64        32               ____________________                 ________________________________________________________________ |
  |                    /             ____________________                                           /                                                      /             ____________________                                        /            _______  | |                    /                                                      /             ____________________                                        /            _______              /             ____________________                               | |                    /             ____________________                                           /                                               /            _______                 /             ____________________                                | |                    /             ____________________                                           /                                               /            _______                 /             ____________________                                |
  |                   /             /            _______                                           /                                                      /             /            _______                                        /    25   5*\/ 15215   | |                   /                                                      /             /            _______                                        /    25   5*\/ 15215              /             /            _______                                | |                   /             /            _______                                           /                                               /    25   5*\/ 15215                 /             /            _______                                 | |                   /             /            _______                                           /                                               /    25   5*\/ 15215                 /             /            _______                                 |
  |                  /   25        /    25   5*\/ 15215                 115                       /                                                      /   25        /    25   5*\/ 15215                 115                8*3 /   - -- + -----------  | |                  /                                                      /   25        /    25   5*\/ 15215                 115                8*3 /   - -- + -----------            /   25        /    25   5*\/ 15215                 115             | |                  /   25        /    25   5*\/ 15215                 115                       /                                           8*3 /   - -- + -----------               /   25        /    25   5*\/ 15215                 115              | |                  /   25        /    25   5*\/ 15215                 115                       /                                           8*3 /   - -- + -----------               /   25        /    25   5*\/ 15215                 115              |
  |                 /    -- + 2*3 /   - -- + -----------  - ---------------------------          /                                            256*      /    -- + 2*3 /   - -- + -----------  - ---------------------------      \/      64        32      | |                 /                                            256*      /    -- + 2*3 /   - -- + -----------  - ---------------------------      \/      64        32               /    -- + 2*3 /   - -- + -----------  - --------------------------- | |                 /    -- + 2*3 /   - -- + -----------  - ---------------------------          /                                              \/      64        32        256*      /    -- + 2*3 /   - -- + -----------  - ---------------------------  | |                 /    -- + 2*3 /   - -- + -----------  - ---------------------------          /                                              \/      64        32        256*      /    -- + 2*3 /   - -- + -----------  - ---------------------------  |
  |                /     64     \/      64        32               ____________________         /                                                      /     64     \/      64        32               ____________________                                | |                /                                                      /     64     \/      64        32               ____________________                                        /     64     \/      64        32               ____________________ | |                /     64     \/      64        32               ____________________         /                                                                                    /     64     \/      64        32               ____________________  | |                /     64     \/      64        32               ____________________         /                                                                                    /     64     \/      64        32               ____________________  |
  |               /                                               /            _______         /                                                      /                                               /            _______                                 | |               /                                                      /                                               /            _______                                        /                                               /            _______  | |               /                                               /            _______         /                                                                                    /                                               /            _______   | |               /                                               /            _______         /                                                                                    /                                               /            _______   |
  |              /                                               /    25   5*\/ 15215         /                                                      /                                               /    25   5*\/ 15215                                  | |              /                                                      /                                               /    25   5*\/ 15215                                        /                                               /    25   5*\/ 15215   | |              /                                               /    25   5*\/ 15215         /                                                                                    /                                               /    25   5*\/ 15215    | |              /                                               /    25   5*\/ 15215         /                                                                                    /                                               /    25   5*\/ 15215    |
  |             /                                           8*3 /   - -- + -----------       /                                                      /                                           8*3 /   - -- + -----------                                 | |             /                                                      /                                           8*3 /   - -- + -----------                                      /                                           8*3 /   - -- + -----------  | |             /                                           8*3 /   - -- + -----------       /                                                                                    /                                           8*3 /   - -- + -----------   | |             /                                           8*3 /   - -- + -----------       /                                                                                    /                                           8*3 /   - -- + -----------   |
  |      5    \/                                              \/      64        32         \/                                                     \/                                              \/      64        32                                     | |      5    \/                                                     \/                                              \/      64        32                                        \/                                              \/      64        32      | |      5    \/                                              \/      64        32         \/                                                                                   \/                                              \/      64        32       | |      5    \/                                              \/      64        32         \/                                                                                   \/                                              \/      64        32       |
x*|x + - -- + -------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------|*|x + - -- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------|*|x + - -- - -------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------|*|x + - -- - -------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------|
  \      16                                       2                                                                                                                       2                                                                                / \      16                                                                                  2                                                                                                                       2                                     / \      16                                       2                                                                                                                       2                                                                                / \      16                                       2                                                                                                                       2                                                                                /

$$x \left(x + \left(- \frac{5}{16} + \frac{\sqrt{- \frac{115}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}}} + \frac{25}{64} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}}}}{2} + \frac{\sqrt{- \frac{2685}{256 \sqrt{- \frac{115}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}}} + \frac{25}{64} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}}}} - 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}} + \frac{25}{32} + \frac{115}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}}}}}{2}\right)\right) \left(x + \left(- \frac{5}{16} + \frac{\sqrt{- \frac{115}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}}} + \frac{25}{64} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}}}}{2} - \frac{\sqrt{- \frac{2685}{256 \sqrt{- \frac{115}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}}} + \frac{25}{64} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}}}} - 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}} + \frac{25}{32} + \frac{115}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}}}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}} + \frac{25}{32} + \frac{115}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}}} + \frac{2685}{256 \sqrt{- \frac{115}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}}} + \frac{25}{64} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}}}}}}{2} - \frac{5}{16} - \frac{\sqrt{- \frac{115}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}}} + \frac{25}{64} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}}}}{2}\right)\right) \left(x + \left(- \frac{5}{16} - \frac{\sqrt{- \frac{115}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}}} + \frac{25}{64} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}} + \frac{25}{32} + \frac{115}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}}} + \frac{2685}{256 \sqrt{- \frac{115}{8 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}}} + \frac{25}{64} + 2 \sqrt[3]{- \frac{25}{64} + \frac{5 \sqrt{15215}}{32}}}}}}{2}\right)\right)$$

Комбинаторика

  /                3      4\
x*\-80 - 20*x - 5*x  + 4*x /
----------------------------
             20             

$$\frac{x \left(4 x^{4} - 5 x^{3} - 20 x - 80\right)}{20}$$