Factorizar el polinomio x^9+1

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                /       /pi\        /pi\     ___    /pi\       ___    /pi\\ /       /pi\     ___    /pi\        /pi\       ___    /pi\\
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                |    cos|--|   I*sin|--|   \/ 3 *sin|--|   I*\/ 3 *cos|--|| |    cos|--|   \/ 3 *sin|--|   I*sin|--|   I*\/ 3 *cos|--||
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$$\left(x + \left(\sin^{2}{\left(\frac{\pi}{9} \right)} + \cos^{2}{\left(\frac{\pi}{9} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{\pi}{9} \right)} - i \sin{\left(\frac{\pi}{9} \right)}\right)\right) \left(x + \left(- \sin^{2}{\left(\frac{\pi}{9} \right)} + \cos^{2}{\left(\frac{\pi}{9} \right)} + 2 i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)} + \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{2 \pi}{9} \right)} - i \sin{\left(\frac{2 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)} - i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)} - \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{2 \pi}{9} \right)} - i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)} + i \sin{\left(\frac{2 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)} + \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{4 \pi}{9} \right)} - i \sin{\left(\frac{4 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)} - i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}\right)\right) \left(x + \left(- \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{4 \pi}{9} \right)} - \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)} - i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)} + i \sin{\left(\frac{4 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}\right)\right) \left(x + \left(\frac{\sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{2} + \frac{\cos{\left(\frac{\pi}{9} \right)}}{2} - \frac{\sqrt{3} i \cos{\left(\frac{\pi}{9} \right)}}{2} + \frac{i \sin{\left(\frac{\pi}{9} \right)}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{2} + \frac{\cos{\left(\frac{\pi}{9} \right)}}{2} + \frac{i \sin{\left(\frac{\pi}{9} \right)}}{2} + \frac{\sqrt{3} i \cos{\left(\frac{\pi}{9} \right)}}{2}\right)\right)$$

((((((((x - i*sin(pi/9) - cos(pi/9))*(x + cos(pi/9)^2 + sin(pi/9)^2))*(x - sin(pi/9)^2 + cos(pi/9)^2 + 2*i*cos(pi/9)*sin(pi/9)))*(x - cos(pi/9)*cos(2*pi/9) + sin(pi/9)*sin(2*pi/9) - i*cos(pi/9)*sin(2*pi/9) - i*cos(2*pi/9)*sin(pi/9)))*(x - cos(pi/9)*cos(2*pi/9) - sin(pi/9)*sin(2*pi/9) - i*cos(2*pi/9)*sin(pi/9) + i*cos(pi/9)*sin(2*pi/9)))*(x - cos(pi/9)*cos(4*pi/9) + sin(pi/9)*sin(4*pi/9) - i*cos(pi/9)*sin(4*pi/9) - i*cos(4*pi/9)*sin(pi/9)))*(x - cos(pi/9)*cos(4*pi/9) - sin(pi/9)*sin(4*pi/9) - i*cos(4*pi/9)*sin(pi/9) + i*cos(pi/9)*sin(4*pi/9)))*(x + cos(pi/9)/2 + i*sin(pi/9)/2 + sqrt(3)*sin(pi/9)/2 - i*sqrt(3)*cos(pi/9)/2))*(x + cos(pi/9)/2 - sqrt(3)*sin(pi/9)/2 + i*sin(pi/9)/2 + i*sqrt(3)*cos(pi/9)/2)