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Simplificación de expresiones/ Descomposición de multiplicadores/ x^7+1

Factorizar el polinomio x^7+1

Expresión a simplificar:

Solución

Ha introducido [src] 
 7    
x  + 1
x7+1x^{7} + 1 
x^7 + 1
Factorización [src] 
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|x + - I*sin|--| - cos|--||*|x + cos |--| + sin |--||*|x + - sin |--| + cos |--| + 2*I*cos|--|*sin|--||*|x + - cos|--|*cos|----| + sin|--|*sin|----| - I*cos|--|*sin|----| - I*cos|----|*sin|--||*|x + - cos|--|*cos|----| - sin|--|*sin|----| - I*cos|----|*sin|--| + I*cos|--|*sin|----||*|x + cos|--|*cos|----| + sin|--|*sin|----| - I*cos|--|*sin|----| + I*cos|----|*sin|--||*|x + - sin|--|*sin|----| + cos|--|*cos|----| + I*cos|--|*sin|----| + I*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+(sin⁡2(π7)+cos⁡2(π7)))(x+(−cos⁡(π7)−isin⁡(π7)))(x+(−sin⁡2(π7)+cos⁡2(π7)+2isin⁡(π7)cos⁡(π7)))(x+(−cos⁡(π7)cos⁡(2π7)+sin⁡(π7)sin⁡(2π7)−isin⁡(2π7)cos⁡(π7)−isin⁡(π7)cos⁡(2π7)))(x+(−cos⁡(π7)cos⁡(2π7)−sin⁡(π7)sin⁡(2π7)−isin⁡(π7)cos⁡(2π7)+isin⁡(2π7)cos⁡(π7)))(x+(cos⁡(π7)cos⁡(3π7)+sin⁡(π7)sin⁡(3π7)−isin⁡(3π7)cos⁡(π7)+isin⁡(π7)cos⁡(3π7)))(x+(−sin⁡(π7)sin⁡(3π7)+cos⁡(π7)cos⁡(3π7)+isin⁡(π7)cos⁡(3π7)+isin⁡(3π7)cos⁡(π7)))\left(x + \left(\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\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(- \sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)} + 2 i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)} + \sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{2 \pi}{7} \right)} - i \sin{\left(\frac{2 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)} - i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)} - \sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{2 \pi}{7} \right)} - i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)} + i \sin{\left(\frac{2 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)} + \sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{3 \pi}{7} \right)} - i \sin{\left(\frac{3 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)} + i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)}\right)\right) \left(x + \left(- \sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{3 \pi}{7} \right)} + \cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)} + i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)} + i \sin{\left(\frac{3 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}\right)\right) 
((((((x - i*sin(pi/7) - cos(pi/7))*(x + cos(pi/7)^2 + sin(pi/7)^2))*(x - sin(pi/7)^2 + cos(pi/7)^2 + 2*i*cos(pi/7)*sin(pi/7)))*(x - cos(pi/7)*cos(2*pi/7) + sin(pi/7)*sin(2*pi/7) - i*cos(pi/7)*sin(2*pi/7) - i*cos(2*pi/7)*sin(pi/7)))*(x - cos(pi/7)*cos(2*pi/7) - sin(pi/7)*sin(2*pi/7) - i*cos(2*pi/7)*sin(pi/7) + i*cos(pi/7)*sin(2*pi/7)))*(x + cos(pi/7)*cos(3*pi/7) + sin(pi/7)*sin(3*pi/7) - i*cos(pi/7)*sin(3*pi/7) + i*cos(3*pi/7)*sin(pi/7)))*(x - sin(pi/7)*sin(3*pi/7) + cos(pi/7)*cos(3*pi/7) + i*cos(pi/7)*sin(3*pi/7) + i*cos(3*pi/7)*sin(pi/7))
Respuesta numérica [src] 
1.0 + x^7
1.0 + x^7
Combinatoria [src] 
        /     2    4    6        3    5\
(1 + x)*\1 + x  + x  + x  - x - x  - x /
(x+1)(x6−x5+x4−x3+x2−x+1)\left(x + 1\right) \left(x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1\right) 
(1 + x)*(1 + x^2 + x^4 + x^6 - x - x^3 - x^5)
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