Разложить многочлен на множители x^4-4*x^3+5*x^2+10*x-10

Объединение рациональных выражений

-10 + x*(10 + x*(5 + x*(-4 + x)))

$$x \left(x \left(x \left(x - 4\right) + 5\right) + 10\right) - 10$$

Комбинаторика

       4      3      2       
-10 + x  - 4*x  + 5*x  + 10*x

$$x^{4} - 4 x^{3} + 5 x^{2} + 10 x - 10$$

Разложение на множители

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|                                                                                                /   4                                      24                                           /  2015   5*\/ 4494                  25             | |                                                                                                /   4                                      24                                           /  2015   5*\/ 4494                  25             | |                     /   4        /  2015   5*\/ 4494                                        24                                                   25                                                                                        | |                                                                                                /   4        /  2015   5*\/ 4494                                        24                                                   25             |
|                                                                                               /    - - ------------------------------------------------------------------------ - 2*3 /   ---- + ----------  - --------------------------- | |                                                                                               /    - - ------------------------------------------------------------------------ - 2*3 /   ---- + ----------  - --------------------------- | |                    /    - - 2*3 /   ---- + ----------  + ------------------------------------------------------------------------ - ---------------------------                                                                            | |                                                                                               /    - - 2*3 /   ---- + ----------  + ------------------------------------------------------------------------ - --------------------------- |
|                   ______________________________________________________________             /     3             ______________________________________________________________     \/    216        36                ___________________ | |                   ______________________________________________________________             /     3             ______________________________________________________________     \/    216        36                ___________________ | |                   /     3     \/    216        36                  ______________________________________________________________           ___________________              ______________________________________________________________| |                   ______________________________________________________________             /     3     \/    216        36                  ______________________________________________________________           ___________________ |
|                  /            ___________________                                           /                   /            ___________________                                                                      /            ______  | |                  /            ___________________                                           /                   /            ___________________                                                                      /            ______  | |                  /                                                /            ___________________                                         /            ______              /            ___________________                               | |                  /            ___________________                                           /                                                /            ___________________                                         /            ______  |
|                 /            /            ______                                           /                   /            /            ______                                                                      /  2015   5*\/ 4494   | |                 /            /            ______                                           /                   /            /            ______                                                                      /  2015   5*\/ 4494   | |                 /                                                /            /            ______                                         /  2015   5*\/ 4494              /            /            ______                                | |                 /            /            ______                                           /                                                /            /            ______                                         /  2015   5*\/ 4494   |
|                /   2        /  2015   5*\/ 4494                  25                       /                   /   2        /  2015   5*\/ 4494                  25                                             18*3 /   ---- + ----------  | |                /   2        /  2015   5*\/ 4494                  25                       /                   /   2        /  2015   5*\/ 4494                  25                                             18*3 /   ---- + ----------  | |                /                                                /   2        /  2015   5*\/ 4494                  25                18*3 /   ---- + ----------            /   2        /  2015   5*\/ 4494                  25             | |                /   2        /  2015   5*\/ 4494                  25                       /                                                /   2        /  2015   5*\/ 4494                  25                18*3 /   ---- + ----------  |
|               /    - + 2*3 /   ---- + ----------  + ---------------------------          /                   /    - + 2*3 /   ---- + ----------  + ---------------------------                                    \/    216        36      | |               /    - + 2*3 /   ---- + ----------  + ---------------------------          /                   /    - + 2*3 /   ---- + ----------  + ---------------------------                                    \/    216        36      | |               /                                                /    - + 2*3 /   ---- + ----------  + ---------------------------       \/    216        36               /    - + 2*3 /   ---- + ----------  + --------------------------- | |               /    - + 2*3 /   ---- + ----------  + ---------------------------          /                                                /    - + 2*3 /   ---- + ----------  + ---------------------------       \/    216        36      |
|              /     3     \/    216        36                ___________________         /                   /     3     \/    216        36                ___________________                                                             | |              /     3     \/    216        36                ___________________         /                   /     3     \/    216        36                ___________________                                                             | |              /                                                /     3     \/    216        36                ___________________                                        /     3     \/    216        36                ___________________ | |              /     3     \/    216        36                ___________________         /                                                /     3     \/    216        36                ___________________                                |
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|            /                                              /  2015   5*\/ 4494         /                   /                                              /  2015   5*\/ 4494                                                               | |            /                                              /  2015   5*\/ 4494         /                   /                                              /  2015   5*\/ 4494                                                               | |            /                                                /                                              /  2015   5*\/ 4494                                        /                                              /  2015   5*\/ 4494   | |            /                                              /  2015   5*\/ 4494         /                                                /                                              /  2015   5*\/ 4494                                  |
|           /                                         18*3 /   ---- + ----------       /                   /                                         18*3 /   ---- + ----------                                                              | |           /                                         18*3 /   ---- + ----------       /                   /                                         18*3 /   ---- + ----------                                                              | |           /                                                /                                         18*3 /   ---- + ----------                                      /                                         18*3 /   ---- + ----------  | |           /                                         18*3 /   ---- + ----------       /                                                /                                         18*3 /   ---- + ----------                                 |
|         \/                                             \/    216        36         \/                  \/                                             \/    216        36                                                                  | |         \/                                             \/    216        36         \/                  \/                                             \/    216        36                                                                  | |         \/                                               \/                                             \/    216        36                                        \/                                             \/    216        36      | |         \/                                             \/    216        36         \/                                               \/                                             \/    216        36                                     |
|x + -1 - ------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------------------------------|*|x + -1 - ------------------------------------------------------------------------ - --------------------------------------------------------------------------------------------------------------------------------------------------------|*|x + -1 - -------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------|*|x + -1 + ------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------------------------------|
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$$\left(x + \left(- \frac{\sqrt{\frac{25}{18 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}}} + \frac{2}{3} + 2 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}}}}{2} - 1 - \frac{\sqrt{- \frac{24}{\sqrt{\frac{25}{18 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}}} + \frac{2}{3} + 2 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}}}} - 2 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}} - \frac{25}{18 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}}} + \frac{4}{3}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{\frac{25}{18 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}}} + \frac{2}{3} + 2 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}}}}{2} - 1 + \frac{\sqrt{- \frac{24}{\sqrt{\frac{25}{18 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}}} + \frac{2}{3} + 2 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}}}} - 2 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}} - \frac{25}{18 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}}} + \frac{4}{3}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}} - \frac{25}{18 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}}} + \frac{4}{3} + \frac{24}{\sqrt{\frac{25}{18 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}}} + \frac{2}{3} + 2 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}}}}}}{2} - 1 + \frac{\sqrt{\frac{25}{18 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}}} + \frac{2}{3} + 2 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}}}}{2}\right)\right) \left(x + \left(-1 + \frac{\sqrt{- 2 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}} - \frac{25}{18 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}}} + \frac{4}{3} + \frac{24}{\sqrt{\frac{25}{18 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}}} + \frac{2}{3} + 2 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}}}}}}{2} + \frac{\sqrt{\frac{25}{18 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}}} + \frac{2}{3} + 2 \sqrt[3]{\frac{5 \sqrt{4494}}{36} + \frac{2015}{216}}}}{2}\right)\right)$$