Разложить многочлен на множители 7*x^5+1

Разложение на множители

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           |                                     /       ___ | |                                     /       ___                     /       ___ | |                        /       ___               /       ___             /       ___      /       ___                     /       ___                     /       ___ | |                      /       ___      /       ___               /       ___               /       ___                     /       ___                     /       ___ |
           |                             4/5    /  5   \/ 5  | |                             4/5    /  5   \/ 5         ___  4/5    /  5   \/ 5  | |                4/5    /  5   \/ 5        4/5    /  5   \/ 5      4/5    /  5   \/ 5      /  5   \/ 5         ___  4/5    /  5   \/ 5         ___  4/5    /  5   \/ 5  | |              4/5    /  5   \/ 5      /  5   \/ 5        4/5    /  5   \/ 5        4/5    /  5   \/ 5         ___  4/5    /  5   \/ 5         ___  4/5    /  5   \/ 5  |
/     4/5\ |       4/5     ___  4/5   I*7   *  /   - - ----- | |       4/5     ___  4/5   I*7   *  /   - - -----    I*\/ 5 *7   *  /   - - ----- | |       4/5   I*7   *  /   - - -----    I*7   *  /   - + -----    7   *  /   - - ----- *  /   - + -----    I*\/ 5 *7   *  /   - + -----    I*\/ 5 *7   *  /   - - ----- | |       4/5   7   *  /   - - ----- *  /   - + -----    I*7   *  /   - - -----    I*7   *  /   - + -----    I*\/ 5 *7   *  /   - - -----    I*\/ 5 *7   *  /   - + ----- |
|    7   | |      7      \/ 5 *7             \/    8     8   | |      7      \/ 5 *7             \/    8     8                   \/    8     8   | |      7             \/    8     8             \/    8     8           \/    8     8    \/    8     8                   \/    8     8                   \/    8     8   | |      7           \/    8     8    \/    8     8             \/    8     8             \/    8     8                   \/    8     8                   \/    8     8   |
|x + ----|*|x + - ---- - ---------- - -----------------------|*|x + - ---- + ---------- + ----------------------- + -----------------------------|*|x + - ---- + ----------------------- + ----------------------- - -------------------------------------- + ----------------------------- - -----------------------------|*|x + - ---- + -------------------------------------- + ----------------------- - ----------------------- - ----------------------------- - -----------------------------|
\     7  / \       28        28                  7           / \       28        28                  14                           14             / \       28               28                        28                               7                                    28                              28             / \       28                      7                                 28                        28                           28                              28             /

$$\left(x + \frac{7^{\frac{4}{5}}}{7}\right) \left(x + \left(- \frac{\sqrt{5} \cdot 7^{\frac{4}{5}}}{28} - \frac{7^{\frac{4}{5}}}{28} - \frac{7^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{7}\right)\right) \left(x + \left(- \frac{7^{\frac{4}{5}}}{28} + \frac{\sqrt{5} \cdot 7^{\frac{4}{5}}}{28} + \frac{7^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{14} + \frac{\sqrt{5} \cdot 7^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{14}\right)\right) \left(x + \left(- \frac{7^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{7} - \frac{7^{\frac{4}{5}}}{28} - \frac{\sqrt{5} \cdot 7^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{28} + \frac{7^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{28} + \frac{7^{\frac{4}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{28} + \frac{\sqrt{5} \cdot 7^{\frac{4}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{28}\right)\right) \left(x + \left(- \frac{7^{\frac{4}{5}}}{28} + \frac{7^{\frac{4}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{7} - \frac{\sqrt{5} \cdot 7^{\frac{4}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{28} - \frac{\sqrt{5} \cdot 7^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{28} - \frac{7^{\frac{4}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{28} + \frac{7^{\frac{4}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{28}\right)\right)$$