Factor polynomial x^8+2*x

  /      7 ___    /pi\     7 ___    /pi\\ /    7 ___    2/pi\   7 ___    2/pi\\ /      7 ___    2/pi\   7 ___    2/pi\       7 ___    /pi\    /pi\\ /      7 ___    /pi\    /2*pi\   7 ___    /pi\    /2*pi\     7 ___    /pi\    /2*pi\     7 ___    /2*pi\    /pi\\ /      7 ___    /pi\    /2*pi\   7 ___    /pi\    /2*pi\     7 ___    /2*pi\    /pi\     7 ___    /pi\    /2*pi\\ /    7 ___    /pi\    /3*pi\   7 ___    /pi\    /3*pi\     7 ___    /pi\    /3*pi\     7 ___    /3*pi\    /pi\\ /      7 ___    /pi\    /3*pi\   7 ___    /pi\    /3*pi\     7 ___    /pi\    /3*pi\     7 ___    /3*pi\    /pi\\
x*|x + - \/ 2 *cos|--| - I*\/ 2 *sin|--||*|x + \/ 2 *cos |--| + \/ 2 *sin |--||*|x + - \/ 2 *sin |--| + \/ 2 *cos |--| + 2*I*\/ 2 *cos|--|*sin|--||*|x + - \/ 2 *cos|--|*cos|----| + \/ 2 *sin|--|*sin|----| - I*\/ 2 *cos|--|*sin|----| - I*\/ 2 *cos|----|*sin|--||*|x + - \/ 2 *cos|--|*cos|----| - \/ 2 *sin|--|*sin|----| - I*\/ 2 *cos|----|*sin|--| + I*\/ 2 *cos|--|*sin|----||*|x + \/ 2 *cos|--|*cos|----| + \/ 2 *sin|--|*sin|----| - I*\/ 2 *cos|--|*sin|----| + I*\/ 2 *cos|----|*sin|--||*|x + - \/ 2 *sin|--|*sin|----| + \/ 2 *cos|--|*cos|----| + I*\/ 2 *cos|--|*sin|----| + I*\/ 2 *cos|----|*sin|--||
  \               \7 /              \7 // \              \7 /             \7 // \                \7 /             \7 /                \7 /    \7 // \               \7 /    \ 7  /            \7 /    \ 7  /              \7 /    \ 7  /              \ 7  /    \7 // \               \7 /    \ 7  /            \7 /    \ 7  /              \ 7  /    \7 /              \7 /    \ 7  // \             \7 /    \ 7  /            \7 /    \ 7  /              \7 /    \ 7  /              \ 7  /    \7 // \               \7 /    \ 7  /            \7 /    \ 7  /              \7 /    \ 7  /              \ 7  /    \7 //

$$x \left(x + \left(- \sqrt[7]{2} \cos{\left(\frac{\pi}{7} \right)} - \sqrt[7]{2} i \sin{\left(\frac{\pi}{7} \right)}\right)\right) \left(x + \left(\sqrt[7]{2} \sin^{2}{\left(\frac{\pi}{7} \right)} + \sqrt[7]{2} \cos^{2}{\left(\frac{\pi}{7} \right)}\right)\right) \left(x + \left(- \sqrt[7]{2} \sin^{2}{\left(\frac{\pi}{7} \right)} + \sqrt[7]{2} \cos^{2}{\left(\frac{\pi}{7} \right)} + 2 \sqrt[7]{2} i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}\right)\right) \left(x + \left(- \sqrt[7]{2} \cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)} + \sqrt[7]{2} \sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{2 \pi}{7} \right)} - \sqrt[7]{2} i \sin{\left(\frac{2 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)} - \sqrt[7]{2} i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)}\right)\right) \left(x + \left(- \sqrt[7]{2} \cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)} - \sqrt[7]{2} \sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{2 \pi}{7} \right)} - \sqrt[7]{2} i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)} + \sqrt[7]{2} i \sin{\left(\frac{2 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}\right)\right) \left(x + \left(\sqrt[7]{2} \cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)} + \sqrt[7]{2} \sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{3 \pi}{7} \right)} - \sqrt[7]{2} i \sin{\left(\frac{3 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)} + \sqrt[7]{2} i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)}\right)\right) \left(x + \left(- \sqrt[7]{2} \sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{3 \pi}{7} \right)} + \sqrt[7]{2} \cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)} + \sqrt[7]{2} i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)} + \sqrt[7]{2} i \sin{\left(\frac{3 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}\right)\right)$$

((((((x*(x - 2^(1/7)*cos(pi/7) - i*2^(1/7)*sin(pi/7)))*(x + 2^(1/7)*cos(pi/7)^2 + 2^(1/7)*sin(pi/7)^2))*(x - 2^(1/7)*sin(pi/7)^2 + 2^(1/7)*cos(pi/7)^2 + 2*i*2^(1/7)*cos(pi/7)*sin(pi/7)))*(x - 2^(1/7)*cos(pi/7)*cos(2*pi/7) + 2^(1/7)*sin(pi/7)*sin(2*pi/7) - i*2^(1/7)*cos(pi/7)*sin(2*pi/7) - i*2^(1/7)*cos(2*pi/7)*sin(pi/7)))*(x - 2^(1/7)*cos(pi/7)*cos(2*pi/7) - 2^(1/7)*sin(pi/7)*sin(2*pi/7) - i*2^(1/7)*cos(2*pi/7)*sin(pi/7) + i*2^(1/7)*cos(pi/7)*sin(2*pi/7)))*(x + 2^(1/7)*cos(pi/7)*cos(3*pi/7) + 2^(1/7)*sin(pi/7)*sin(3*pi/7) - i*2^(1/7)*cos(pi/7)*sin(3*pi/7) + i*2^(1/7)*cos(3*pi/7)*sin(pi/7)))*(x - 2^(1/7)*sin(pi/7)*sin(3*pi/7) + 2^(1/7)*cos(pi/7)*cos(3*pi/7) + i*2^(1/7)*cos(pi/7)*sin(3*pi/7) + i*2^(1/7)*cos(3*pi/7)*sin(pi/7))