Разложить многочлен на множители x^10+x^5+7

Объединение рациональных выражений

     5 /     5\
7 + x *\1 + x /

$$x^{5} \left(x^{5} + 1\right) + 7$$

Комбинаторика

     5    10
7 + x  + x  

$$x^{10} + x^{5} + 7$$

Разложение на множители

                                                                                                                                                        /             /      /    ___\     \                                                                 /      /    ___\     \                  /      /    ___\     \                                                                         /      /    ___\     \\ /             /      /    ___\     \                                                                 /      /    ___\     \                  /      /    ___\     \                                                                         /      /    ___\     \\ /             /      /    ___\     \                                                                 /      /    ___\     \                  /      /    ___\     \                                                                         /      /    ___\     \\ /             /      /    ___\     \                                                                     /      /    ___\     \              /      /    ___\     \                                                                         /      /    ___\     \\ /             /      /    ___\     \                                                                     /      /    ___\     \              /      /    ___\     \                                                                         /      /    ___\     \\ /             /      /    ___\     \                                                                 /      /    ___\     \                  /      /    ___\     \                                                                         /      /    ___\     \\ /             /      /    ___\     \                                                                 /      /    ___\     \                  /      /    ___\     \                                                                         /      /    ___\     \\ /             /      /    ___\     \                                                                 /      /    ___\     \                  /      /    ___\     \                                                                         /      /    ___\     \\
                                                                                                                                                        |    10___    |  atan\3*\/ 3 /   pi|              ___________                               10___    |  atan\3*\/ 3 /   pi|     ___ 10___    |  atan\3*\/ 3 /   pi|                ___________                                 ___ 10___    |  atan\3*\/ 3 /   pi|| |    10___    |  atan\3*\/ 3 /   pi|              ___________                               10___    |  atan\3*\/ 3 /   pi|     ___ 10___    |  atan\3*\/ 3 /   pi|                ___________                                 ___ 10___    |  atan\3*\/ 3 /   pi|| |    10___    |  atan\3*\/ 3 /   pi|              ___________                               10___    |  atan\3*\/ 3 /   pi|     ___ 10___    |  atan\3*\/ 3 /   pi|                ___________                                 ___ 10___    |  atan\3*\/ 3 /   pi|| |    10___    |  atan\3*\/ 3 /   pi|              ___________                               ___ 10___    |  atan\3*\/ 3 /   pi|     10___    |  atan\3*\/ 3 /   pi|                ___________                                 ___ 10___    |  atan\3*\/ 3 /   pi|| |    10___    |  atan\3*\/ 3 /   pi|              ___________                               ___ 10___    |  atan\3*\/ 3 /   pi|     10___    |  atan\3*\/ 3 /   pi|                ___________                                 ___ 10___    |  atan\3*\/ 3 /   pi|| |    10___    |  atan\3*\/ 3 /   pi|              ___________                               10___    |  atan\3*\/ 3 /   pi|     ___ 10___    |  atan\3*\/ 3 /   pi|                ___________                                 ___ 10___    |  atan\3*\/ 3 /   pi|| |    10___    |  atan\3*\/ 3 /   pi|              ___________                               10___    |  atan\3*\/ 3 /   pi|     ___ 10___    |  atan\3*\/ 3 /   pi|                ___________                                 ___ 10___    |  atan\3*\/ 3 /   pi|| |    10___    |  atan\3*\/ 3 /   pi|              ___________                               10___    |  atan\3*\/ 3 /   pi|     ___ 10___    |  atan\3*\/ 3 /   pi|                ___________                                 ___ 10___    |  atan\3*\/ 3 /   pi||
/               /      /    ___\     \              /      /    ___\     \\ /               /      /    ___\     \              /      /    ___\     \\ |    \/ 7 *cos|- ------------- + --|             /       ___     /      /    ___\     \   I*\/ 7 *sin|- ------------- + --|   \/ 5 *\/ 7 *cos|- ------------- + --|               /       ___     /      /    ___\     \   I*\/ 5 *\/ 7 *sin|- ------------- + --|| |    \/ 7 *cos|- ------------- + --|             /       ___     /      /    ___\     \   I*\/ 7 *sin|- ------------- + --|   \/ 5 *\/ 7 *cos|- ------------- + --|               /       ___     /      /    ___\     \   I*\/ 5 *\/ 7 *sin|- ------------- + --|| |    \/ 7 *cos|- ------------- + --|             /       ___     /      /    ___\     \   I*\/ 7 *sin|- ------------- + --|   \/ 5 *\/ 7 *cos|- ------------- + --|               /       ___     /      /    ___\     \   I*\/ 5 *\/ 7 *sin|- ------------- + --|| |    \/ 7 *cos|- ------------- + --|             /       ___     /      /    ___\     \   \/ 5 *\/ 7 *cos|- ------------- + --|   I*\/ 7 *sin|- ------------- + --|               /       ___     /      /    ___\     \   I*\/ 5 *\/ 7 *sin|- ------------- + --|| |    \/ 7 *cos|- ------------- + --|             /       ___     /      /    ___\     \   \/ 5 *\/ 7 *cos|- ------------- + --|   I*\/ 7 *sin|- ------------- + --|               /       ___     /      /    ___\     \   I*\/ 5 *\/ 7 *sin|- ------------- + --|| |    \/ 7 *cos|- ------------- + --|             /       ___     /      /    ___\     \   I*\/ 7 *sin|- ------------- + --|   \/ 5 *\/ 7 *cos|- ------------- + --|               /       ___     /      /    ___\     \   I*\/ 5 *\/ 7 *sin|- ------------- + --|| |    \/ 7 *cos|- ------------- + --|             /       ___     /      /    ___\     \   I*\/ 7 *sin|- ------------- + --|   \/ 5 *\/ 7 *cos|- ------------- + --|               /       ___     /      /    ___\     \   I*\/ 5 *\/ 7 *sin|- ------------- + --|| |    \/ 7 *cos|- ------------- + --|             /       ___     /      /    ___\     \   I*\/ 7 *sin|- ------------- + --|   \/ 5 *\/ 7 *cos|- ------------- + --|               /       ___     /      /    ___\     \   I*\/ 5 *\/ 7 *sin|- ------------- + --||
|      10___    |  atan\3*\/ 3 /   pi|     10___    |  atan\3*\/ 3 /   pi|| |      10___    |  atan\3*\/ 3 /   pi|     10___    |  atan\3*\/ 3 /   pi|| |             \        5         5 /   10___    /  5   \/ 5      |  atan\3*\/ 3 /   pi|              \        5         5 /                  \        5         5 /     10___    /  5   \/ 5      |  atan\3*\/ 3 /   pi|                    \        5         5 /| |             \        5         5 /   10___    /  5   \/ 5      |  atan\3*\/ 3 /   pi|              \        5         5 /                  \        5         5 /     10___    /  5   \/ 5      |  atan\3*\/ 3 /   pi|                    \        5         5 /| |             \        5         5 /   10___    /  5   \/ 5      |  atan\3*\/ 3 /   pi|              \        5         5 /                  \        5         5 /     10___    /  5   \/ 5      |  atan\3*\/ 3 /   pi|                    \        5         5 /| |             \        5         5 /   10___    /  5   \/ 5      |  atan\3*\/ 3 /   pi|                  \        5         5 /              \        5         5 /     10___    /  5   \/ 5      |  atan\3*\/ 3 /   pi|                    \        5         5 /| |             \        5         5 /   10___    /  5   \/ 5      |  atan\3*\/ 3 /   pi|                  \        5         5 /              \        5         5 /     10___    /  5   \/ 5      |  atan\3*\/ 3 /   pi|                    \        5         5 /| |             \        5         5 /   10___    /  5   \/ 5      |  atan\3*\/ 3 /   pi|              \        5         5 /                  \        5         5 /     10___    /  5   \/ 5      |  atan\3*\/ 3 /   pi|                    \        5         5 /| |             \        5         5 /   10___    /  5   \/ 5      |  atan\3*\/ 3 /   pi|              \        5         5 /                  \        5         5 /     10___    /  5   \/ 5      |  atan\3*\/ 3 /   pi|                    \        5         5 /| |             \        5         5 /   10___    /  5   \/ 5      |  atan\3*\/ 3 /   pi|              \        5         5 /                  \        5         5 /     10___    /  5   \/ 5      |  atan\3*\/ 3 /   pi|                    \        5         5 /|
|x + - \/ 7 *cos|- ------------- + --| + I*\/ 7 *sin|- ------------- + --||*|x + - \/ 7 *cos|- ------------- + --| - I*\/ 7 *sin|- ------------- + --||*|x + ------------------------------- - \/ 7 *  /   - + ----- *sin|- ------------- + --| - --------------------------------- - ------------------------------------- - I*\/ 7 *  /   - + ----- *cos|- ------------- + --| + ---------------------------------------|*|x + ------------------------------- - \/ 7 *  /   - + ----- *sin|- ------------- + --| + --------------------------------- - ------------------------------------- + I*\/ 7 *  /   - + ----- *cos|- ------------- + --| - ---------------------------------------|*|x + ------------------------------- + \/ 7 *  /   - - ----- *sin|- ------------- + --| + --------------------------------- + ------------------------------------- - I*\/ 7 *  /   - - ----- *cos|- ------------- + --| + ---------------------------------------|*|x + ------------------------------- + \/ 7 *  /   - - ----- *sin|- ------------- + --| + ------------------------------------- - --------------------------------- + I*\/ 7 *  /   - - ----- *cos|- ------------- + --| - ---------------------------------------|*|x + ------------------------------- - \/ 7 *  /   - - ----- *sin|- ------------- + --| + ------------------------------------- - --------------------------------- - I*\/ 7 *  /   - - ----- *cos|- ------------- + --| - ---------------------------------------|*|x + ------------------------------- - \/ 7 *  /   - - ----- *sin|- ------------- + --| + --------------------------------- + ------------------------------------- + I*\/ 7 *  /   - - ----- *cos|- ------------- + --| + ---------------------------------------|*|x + ------------------------------- + \/ 7 *  /   - + ----- *sin|- ------------- + --| + --------------------------------- - ------------------------------------- - I*\/ 7 *  /   - + ----- *cos|- ------------- + --| - ---------------------------------------|*|x + ------------------------------- + \/ 7 *  /   - + ----- *sin|- ------------- + --| - --------------------------------- - ------------------------------------- + I*\/ 7 *  /   - + ----- *cos|- ------------- + --| + ---------------------------------------|
\               \        5         5 /              \        5         5 // \               \        5         5 /              \        5         5 // \                   4                        \/    8     8       \        5         5 /                   4                                     4                             \/    8     8       \        5         5 /                      4                   / \                   4                        \/    8     8       \        5         5 /                   4                                     4                             \/    8     8       \        5         5 /                      4                   / \                   4                        \/    8     8       \        5         5 /                   4                                     4                             \/    8     8       \        5         5 /                      4                   / \                   4                        \/    8     8       \        5         5 /                     4                                     4                           \/    8     8       \        5         5 /                      4                   / \                   4                        \/    8     8       \        5         5 /                     4                                     4                           \/    8     8       \        5         5 /                      4                   / \                   4                        \/    8     8       \        5         5 /                   4                                     4                             \/    8     8       \        5         5 /                      4                   / \                   4                        \/    8     8       \        5         5 /                   4                                     4                             \/    8     8       \        5         5 /                      4                   / \                   4                        \/    8     8       \        5         5 /                   4                                     4                             \/    8     8       \        5         5 /                      4                   /

$$\left(x + \left(- \sqrt[10]{7} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)} - \sqrt[10]{7} i \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}\right)\right) \left(x + \left(- \sqrt[10]{7} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)} + \sqrt[10]{7} i \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}\right)\right) \left(x + \left(- \frac{\sqrt{5} \sqrt[10]{7} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} - \sqrt[10]{7} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)} + \frac{\sqrt[10]{7} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} - \sqrt[10]{7} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)} - \frac{\sqrt[10]{7} i \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} + \frac{\sqrt{5} \sqrt[10]{7} i \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4}\right)\right) \left(x + \left(- \frac{\sqrt{5} \sqrt[10]{7} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} - \sqrt[10]{7} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)} + \frac{\sqrt[10]{7} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} - \frac{\sqrt{5} \sqrt[10]{7} i \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} + \frac{\sqrt[10]{7} i \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} + \sqrt[10]{7} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}\right)\right) \left(x + \left(\sqrt[10]{7} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)} + \frac{\sqrt[10]{7} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} + \frac{\sqrt{5} \sqrt[10]{7} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} - \sqrt[10]{7} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)} + \frac{\sqrt[10]{7} i \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} + \frac{\sqrt{5} \sqrt[10]{7} i \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4}\right)\right) \left(x + \left(\sqrt[10]{7} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)} + \frac{\sqrt[10]{7} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} + \frac{\sqrt{5} \sqrt[10]{7} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} - \frac{\sqrt{5} \sqrt[10]{7} i \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} - \frac{\sqrt[10]{7} i \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} + \sqrt[10]{7} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}\right)\right) \left(x + \left(- \sqrt[10]{7} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)} + \frac{\sqrt[10]{7} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} + \frac{\sqrt{5} \sqrt[10]{7} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} - \sqrt[10]{7} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)} - \frac{\sqrt{5} \sqrt[10]{7} i \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} - \frac{\sqrt[10]{7} i \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4}\right)\right) \left(x + \left(- \sqrt[10]{7} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)} + \frac{\sqrt[10]{7} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} + \frac{\sqrt{5} \sqrt[10]{7} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} + \frac{\sqrt[10]{7} i \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} + \frac{\sqrt{5} \sqrt[10]{7} i \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} + \sqrt[10]{7} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}\right)\right) \left(x + \left(- \frac{\sqrt{5} \sqrt[10]{7} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} + \frac{\sqrt[10]{7} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} + \sqrt[10]{7} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)} - \sqrt[10]{7} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)} - \frac{\sqrt{5} \sqrt[10]{7} i \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} + \frac{\sqrt[10]{7} i \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4}\right)\right) \left(x + \left(- \frac{\sqrt{5} \sqrt[10]{7} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} + \frac{\sqrt[10]{7} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} + \sqrt[10]{7} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)} - \frac{\sqrt[10]{7} i \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} + \frac{\sqrt{5} \sqrt[10]{7} i \sin{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}}{4} + \sqrt[10]{7} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} \cos{\left(- \frac{\operatorname{atan}{\left(3 \sqrt{3} \right)}}{5} + \frac{\pi}{5} \right)}\right)\right)$$