Разложить многочлен на множители 4050*x^4+10215*x^3+2781*x^2+220*x+5600

Объединение рациональных выражений

5600 + x*(220 + 9*x*(309 + 5*x*(227 + 90*x)))

$$x \left(9 x \left(5 x \left(90 x + 227\right) + 309\right) + 220\right) + 5600$$

Разложение на множители

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|                                                                                                                                               /   36697        /  855658331    \/ 678937524534730605                           10116743                                                                                   6963587                                                             | |                                                                                                                                               /   36697        /  855658331    \/ 678937524534730605                           10116743                                                                                   6963587                                                             | |                                                                                                                                               /   36697        /  855658331    \/ 678937524534730605                           10116743                                                                                   6963587                                                             | |                      /   36697        /  855658331    \/ 678937524534730605                           10116743                                                                                   6963587                                                                                                                                                                                      |
|                                                                                                                                              /    ----- - 2*3 /   ---------- + ----------------------  - --------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------ | |                                                                                                                                              /    ----- - 2*3 /   ---------- + ----------------------  - --------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------ | |                                                                                                                                              /    ----- - 2*3 /   ---------- + ----------------------  - --------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------ | |                     /    ----- - 2*3 /   ---------- + ----------------------  - --------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------                                                                                                                          |
|                    ____________________________________________________________________________________________________________             /     16200     \/    2187000000         3542940000                        _____________________________________                     ____________________________________________________________________________________________________________ | |                    ____________________________________________________________________________________________________________             /     16200     \/    2187000000         3542940000                        _____________________________________                     ____________________________________________________________________________________________________________ | |                    ____________________________________________________________________________________________________________             /     16200     \/    2187000000         3542940000                        _____________________________________                     ____________________________________________________________________________________________________________ | |                    /     16200     \/    2187000000         3542940000                        _____________________________________                     ____________________________________________________________________________________________________________              ____________________________________________________________________________________________________________|
|                   /                _____________________________________                                                                   /                                                                          /                ____________________                     /                _____________________________________                                                        | |                   /                _____________________________________                                                                   /                                                                          /                ____________________                     /                _____________________________________                                                        | |                   /                _____________________________________                                                                   /                                                                          /                ____________________                     /                _____________________________________                                                        | |                   /                                                                          /                ____________________                     /                _____________________________________                                                                    /                _____________________________________                                                       |
|                  /                /                ____________________                                                                   /                                                                          /  855658331    \/ 678937524534730605                     /                /                ____________________                                                         | |                  /                /                ____________________                                                                   /                                                                          /  855658331    \/ 678937524534730605                     /                /                ____________________                                                         | |                  /                /                ____________________                                                                   /                                                                          /  855658331    \/ 678937524534730605                     /                /                ____________________                                                         | |                  /                                                                          /  855658331    \/ 678937524534730605                     /                /                ____________________                                                                    /                /                ____________________                                                        |
|                 /   36697        /  855658331    \/ 678937524534730605                           10116743                                /                                                               10935000*3 /   ---------- + ----------------------                   /   36697        /  855658331    \/ 678937524534730605                           10116743                       | |                 /   36697        /  855658331    \/ 678937524534730605                           10116743                                /                                                               10935000*3 /   ---------- + ----------------------                   /   36697        /  855658331    \/ 678937524534730605                           10116743                       | |                 /   36697        /  855658331    \/ 678937524534730605                           10116743                                /                                                               10935000*3 /   ---------- + ----------------------                   /   36697        /  855658331    \/ 678937524534730605                           10116743                       | |                 /                                                               10935000*3 /   ---------- + ----------------------                   /   36697        /  855658331    \/ 678937524534730605                           10116743                                 /   36697        /  855658331    \/ 678937524534730605                           10116743                      |
|                /    ----- + 2*3 /   ---------- + ----------------------  + ---------------------------------------------------          /                                                                         \/    2187000000         3542940000          2916000*      /    ----- + 2*3 /   ---------- + ----------------------  + ---------------------------------------------------  | |                /    ----- + 2*3 /   ---------- + ----------------------  + ---------------------------------------------------          /                                                                         \/    2187000000         3542940000          2916000*      /    ----- + 2*3 /   ---------- + ----------------------  + ---------------------------------------------------  | |                /    ----- + 2*3 /   ---------- + ----------------------  + ---------------------------------------------------          /                                                                         \/    2187000000         3542940000          2916000*      /    ----- + 2*3 /   ---------- + ----------------------  + ---------------------------------------------------  | |                /                                                                         \/    2187000000         3542940000          2916000*      /    ----- + 2*3 /   ---------- + ----------------------  + ---------------------------------------------------           /    ----- + 2*3 /   ---------- + ----------------------  + --------------------------------------------------- |
|               /     32400     \/    2187000000         3542940000                        _____________________________________         /                                                                                                                                    /     32400     \/    2187000000         3542940000                        _____________________________________  | |               /     32400     \/    2187000000         3542940000                        _____________________________________         /                                                                                                                                    /     32400     \/    2187000000         3542940000                        _____________________________________  | |               /     32400     \/    2187000000         3542940000                        _____________________________________         /                                                                                                                                    /     32400     \/    2187000000         3542940000                        _____________________________________  | |               /                                                                                                                                    /     32400     \/    2187000000         3542940000                        _____________________________________          /     32400     \/    2187000000         3542940000                        _____________________________________ |
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|             /                                                                          /  855658331    \/ 678937524534730605         /                                                                                                                                    /                                                                          /  855658331    \/ 678937524534730605    | |             /                                                                          /  855658331    \/ 678937524534730605         /                                                                                                                                    /                                                                          /  855658331    \/ 678937524534730605    | |             /                                                                          /  855658331    \/ 678937524534730605         /                                                                                                                                    /                                                                          /  855658331    \/ 678937524534730605    | |             /                                                                                                                                    /                                                                          /  855658331    \/ 678937524534730605          /                                                                          /  855658331    \/ 678937524534730605   |
|            /                                                               10935000*3 /   ---------- + ----------------------       /                                                                                                                                    /                                                               10935000*3 /   ---------- + ----------------------   | |            /                                                               10935000*3 /   ---------- + ----------------------       /                                                                                                                                    /                                                               10935000*3 /   ---------- + ----------------------   | |            /                                                               10935000*3 /   ---------- + ----------------------       /                                                                                                                                    /                                                               10935000*3 /   ---------- + ----------------------   | |            /                                                                                                                                    /                                                               10935000*3 /   ---------- + ----------------------        /                                                               10935000*3 /   ---------- + ----------------------  |
|    227   \/                                                                         \/    2187000000         3542940000           \/                                                                                                                                   \/                                                                         \/    2187000000         3542940000         | |    227   \/                                                                         \/    2187000000         3542940000           \/                                                                                                                                   \/                                                                         \/    2187000000         3542940000         | |    227   \/                                                                         \/    2187000000         3542940000           \/                                                                                                                                   \/                                                                         \/    2187000000         3542940000         | |    227   \/                                                                                                                                   \/                                                                         \/    2187000000         3542940000            \/                                                                         \/    2187000000         3542940000        |
|x + --- - ---------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|x + --- - ---------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|x + --- + ---------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|x + --- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ----------------------------------------------------------------------------------------------------------------------|
\    360                                                             2                                                                                                                                                                                           2                                                                                                                              / \    360                                                             2                                                                                                                                                                                           2                                                                                                                              / \    360                                                             2                                                                                                                                                                                           2                                                                                                                              / \    360                                                                                                                                2                                                                                                                                                                                           2                                                           /

$$\left(x + \left(- \frac{\sqrt{\frac{10116743}{10935000 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}}} + \frac{36697}{32400} + 2 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}}}}{2} + \frac{227}{360} - \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}} - \frac{6963587}{2916000 \sqrt{\frac{10116743}{10935000 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}}} + \frac{36697}{32400} + 2 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}}}} - \frac{10116743}{10935000 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}}} + \frac{36697}{16200}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{\frac{10116743}{10935000 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}}} + \frac{36697}{32400} + 2 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}}}}{2} + \frac{227}{360} + \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}} - \frac{6963587}{2916000 \sqrt{\frac{10116743}{10935000 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}}} + \frac{36697}{32400} + 2 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}}}} - \frac{10116743}{10935000 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}}} + \frac{36697}{16200}}}{2}\right)\right) \left(x + \left(\frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}} - \frac{10116743}{10935000 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}}} + \frac{6963587}{2916000 \sqrt{\frac{10116743}{10935000 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}}} + \frac{36697}{32400} + 2 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}}}} + \frac{36697}{16200}}}{2} + \frac{227}{360} + \frac{\sqrt{\frac{10116743}{10935000 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}}} + \frac{36697}{32400} + 2 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}} - \frac{10116743}{10935000 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}}} + \frac{6963587}{2916000 \sqrt{\frac{10116743}{10935000 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}}} + \frac{36697}{32400} + 2 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}}}} + \frac{36697}{16200}}}{2} + \frac{227}{360} + \frac{\sqrt{\frac{10116743}{10935000 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}}} + \frac{36697}{32400} + 2 \sqrt[3]{\frac{\sqrt{678937524534730605}}{3542940000} + \frac{855658331}{2187000000}}}}{2}\right)\right)$$

Комбинаторика

                     2         4          3
5600 + 220*x + 2781*x  + 4050*x  + 10215*x 

$$4050 x^{4} + 10215 x^{3} + 2781 x^{2} + 220 x + 5600$$