Factorizar el polinomio a^5+a+1

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                                    |                                                      /  25   3*\/ 69   |  1   I*\/ 3 || |                                                      /  25   3*\/ 69   |  1   I*\/ 3 || |                                      /  25   3*\/ 69  |
/            ___\ /            ___\ |                                                   3 /   -- + -------- *|- - - -------|| |                                                   3 /   -- + -------- *|- - + -------|| |                                   3 /   -- + -------- |
|    1   I*\/ 3 | |    1   I*\/ 3 | |      1                     1                      \/    2       2      \  2      2   /| |      1                     1                      \/    2       2      \  2      2   /| |      1             1              \/    2       2     |
|a + - + -------|*|a + - - -------|*|a + - - + -------------------------------------- + ------------------------------------|*|a + - - + -------------------------------------- + ------------------------------------|*|a + - - + ---------------------- + --------------------|
\    2      2   / \    2      2   / |      3                          _______________                    3                  | |      3                          _______________                    3                  | |      3          _______________            3          |
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                                    |            |  1   I*\/ 3 |    /  25   3*\/ 69                                         | |            |  1   I*\/ 3 |    /  25   3*\/ 69                                         | |               /  25   3*\/ 69                         |
                                    |          3*|- - - -------|*3 /   -- + --------                                        | |          3*|- - + -------|*3 /   -- + --------                                        | |          3*3 /   -- + --------                        |
                                    \            \  2      2   / \/    2       2                                            / \            \  2      2   / \/    2       2                                            / \            \/    2       2                            /

$$\left(a + \left(\frac{1}{2} - \frac{\sqrt{3} i}{2}\right)\right) \left(a + \left(\frac{1}{2} + \frac{\sqrt{3} i}{2}\right)\right) \left(a + \left(- \frac{1}{3} + \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{69}}{2} + \frac{25}{2}}}{3} + \frac{1}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{69}}{2} + \frac{25}{2}}}\right)\right) \left(a + \left(- \frac{1}{3} + \frac{1}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{69}}{2} + \frac{25}{2}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{69}}{2} + \frac{25}{2}}}{3}\right)\right) \left(a + \left(- \frac{1}{3} + \frac{1}{3 \sqrt[3]{\frac{3 \sqrt{69}}{2} + \frac{25}{2}}} + \frac{\sqrt[3]{\frac{3 \sqrt{69}}{2} + \frac{25}{2}}}{3}\right)\right)$$

((((a + 1/2 + i*sqrt(3)/2)*(a + 1/2 - i*sqrt(3)/2))*(a - 1/3 + 1/(3*(-1/2 - i*sqrt(3)/2)*(25/2 + 3*sqrt(69)/2)^(1/3)) + (25/2 + 3*sqrt(69)/2)^(1/3)*(-1/2 - i*sqrt(3)/2)/3))*(a - 1/3 + 1/(3*(-1/2 + i*sqrt(3)/2)*(25/2 + 3*sqrt(69)/2)^(1/3)) + (25/2 + 3*sqrt(69)/2)^(1/3)*(-1/2 + i*sqrt(3)/2)/3))*(a - 1/3 + 1/(3*(25/2 + 3*sqrt(69)/2)^(1/3)) + (25/2 + 3*sqrt(69)/2)^(1/3)/3)