Factor polynomial c^5+1

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        |            ___         /       ___ | |            ___   I*  /   - - -----    I*\/ 5 *  /   - - ----- | |              /       ___      /       ___    I*  /   - - -----    I*  /   - + -----    I*\/ 5 *  /   - + -----    I*\/ 5 *  /   - - ----- | |              /       ___      /       ___    I*  /   - - -----    I*  /   - + -----    I*\/ 5 *  /   - - -----    I*\/ 5 *  /   - + ----- |
        |      1   \/ 5         /  5   \/ 5  | |      1   \/ 5      \/    8     8              \/    8     8   | |      1      /  5   \/ 5      /  5   \/ 5       \/    8     8        \/    8     8              \/    8     8              \/    8     8   | |      1      /  5   \/ 5      /  5   \/ 5       \/    8     8        \/    8     8              \/    8     8              \/    8     8   |
(c + 1)*|c + - - - ----- - I*  /   - - ----- |*|c + - - + ----- + ------------------ + ------------------------|*|c + - - -   /   - - ----- *  /   - + -----  + ------------------ + ------------------ + ------------------------ - ------------------------|*|c + - - +   /   - - ----- *  /   - + -----  + ------------------ - ------------------ - ------------------------ - ------------------------|
        \      4     4       \/    8     8   / \      4     4             2                       2            / \      4   \/    8     8    \/    8     8              4                    4                       4                          4            / \      4   \/    8     8    \/    8     8              4                    4                       4                          4            /

$$\left(c + 1\right) \left(c + \left(- \frac{\sqrt{5}}{4} - \frac{1}{4} - i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(c + \left(- \frac{1}{4} + \frac{\sqrt{5}}{4} + \frac{i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} + \frac{\sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2}\right)\right) \left(c + \left(- \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} - \frac{1}{4} - \frac{\sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{4} + \frac{i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{4} + \frac{i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{4} + \frac{\sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{4}\right)\right) \left(c + \left(- \frac{1}{4} + \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} - \frac{\sqrt{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{4} - \frac{\sqrt{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{4} - \frac{i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{4} + \frac{i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{4}\right)\right)$$

((((c + 1)*(c - 1/4 - sqrt(5)/4 - i*sqrt(5/8 - sqrt(5)/8)))*(c - 1/4 + sqrt(5)/4 + i*sqrt(5/8 - sqrt(5)/8)/2 + i*sqrt(5)*sqrt(5/8 - sqrt(5)/8)/2))*(c - 1/4 - sqrt(5/8 - sqrt(5)/8)*sqrt(5/8 + sqrt(5)/8) + i*sqrt(5/8 - sqrt(5)/8)/4 + i*sqrt(5/8 + sqrt(5)/8)/4 + i*sqrt(5)*sqrt(5/8 + sqrt(5)/8)/4 - i*sqrt(5)*sqrt(5/8 - sqrt(5)/8)/4))*(c - 1/4 + sqrt(5/8 - sqrt(5)/8)*sqrt(5/8 + sqrt(5)/8) + i*sqrt(5/8 - sqrt(5)/8)/4 - i*sqrt(5/8 + sqrt(5)/8)/4 - i*sqrt(5)*sqrt(5/8 - sqrt(5)/8)/4 - i*sqrt(5)*sqrt(5/8 + sqrt(5)/8)/4)