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Expression simplification/ Factorization polynomials/ x^7-1

Factor polynomial x^7-1

An expression to simplify:

The solution

You have entered [src] 
 7    
x  - 1
$$x^{7} - 1$$ 
x^7 - 1
Factorization [src] 
        /       /pi\        /pi\\ /       /pi\        /pi\\ /         /2*pi\      /2*pi\\ /           /2*pi\      /2*pi\\ /       /3*pi\        /3*pi\\ /       /3*pi\        /3*pi\\
(x - 1)*|x + cos|--| + I*sin|--||*|x + cos|--| - I*sin|--||*|x + I*sin|----| - cos|----||*|x + - I*sin|----| - cos|----||*|x + cos|----| + I*sin|----||*|x + cos|----| - I*sin|----||
        \       \7 /        \7 // \       \7 /        \7 // \         \ 7  /      \ 7  // \           \ 7  /      \ 7  // \       \ 7  /        \ 7  // \       \ 7  /        \ 7  //
$$\left(x - 1\right) \left(x + \left(\cos{\left(\frac{\pi}{7} \right)} + i \sin{\left(\frac{\pi}{7} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{\pi}{7} \right)} - i \sin{\left(\frac{\pi}{7} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{2 \pi}{7} \right)} + i \sin{\left(\frac{2 \pi}{7} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{2 \pi}{7} \right)} - i \sin{\left(\frac{2 \pi}{7} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{3 \pi}{7} \right)} + i \sin{\left(\frac{3 \pi}{7} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{3 \pi}{7} \right)} - i \sin{\left(\frac{3 \pi}{7} \right)}\right)\right)$$ 
((((((x - 1)*(x + cos(pi/7) + i*sin(pi/7)))*(x + cos(pi/7) - i*sin(pi/7)))*(x + i*sin(2*pi/7) - cos(2*pi/7)))*(x - i*sin(2*pi/7) - cos(2*pi/7)))*(x + cos(3*pi/7) + i*sin(3*pi/7)))*(x + cos(3*pi/7) - i*sin(3*pi/7))
Numerical answer [src] 
-1.0 + x^7
-1.0 + x^7
Combinatorics [src] 
         /         2    3    4    5    6\
(-1 + x)*\1 + x + x  + x  + x  + x  + x /
$$\left(x - 1\right) \left(x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1\right)$$ 
(-1 + x)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)
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