Sr Examen

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Simplificación de expresiones/ Descomposición de multiplicadores/ x^6-x^60

Factorizar el polinomio x^6-x^60

Expresión a simplificar:

Solución

Ha introducido [src] 
 6    60
x  - x
−x60+x6- x^{60} + x^{6} 
x^6 - x^60
Factorización [src] 
                  /            ___\ /            ___\ /              ___\ /              ___\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                
                  |    1   I*\/ 3 | |    1   I*\/ 3 | |      1   I*\/ 3 | |      1   I*\/ 3 | /       /pi\        /pi\\ /       /pi\        /pi\\ /         /pi\      /pi\\ /           /pi\      /pi\\ /       /2*pi\        /2*pi\\ /       /2*pi\        /2*pi\\ /         /2*pi\      /2*pi\\ /           /2*pi\      /2*pi\\ /       /pi\        /pi\\ /       /pi\        /pi\\ /         /pi\      /pi\\ /           /pi\      /pi\\ /       /4*pi\        /4*pi\\ /       /4*pi\        /4*pi\\ /         /4*pi\      /4*pi\\ /           /4*pi\      /4*pi\\ /       /5*pi\        /5*pi\\ /       /5*pi\        /5*pi\\ /         /5*pi\      /5*pi\\ /           /5*pi\      /5*pi\\ /       /2*pi\        /2*pi\\ /       /2*pi\        /2*pi\\ /         /2*pi\      /2*pi\\ /           /2*pi\      /2*pi\\ /       /7*pi\        /7*pi\\ /       /7*pi\        /7*pi\\ /         /7*pi\      /7*pi\\ /           /7*pi\      /7*pi\\ /       /8*pi\        /8*pi\\ /       /8*pi\        /8*pi\\ /         /8*pi\      /8*pi\\ /           /8*pi\      /8*pi\\ /       /10*pi\        /10*pi\\ /       /10*pi\        /10*pi\\ /         /10*pi\      /10*pi\\ /           /10*pi\      /10*pi\\ /       /11*pi\        /11*pi\\ /       /11*pi\        /11*pi\\ /         /11*pi\      /11*pi\\ /           /11*pi\      /11*pi\\ /       /4*pi\        /4*pi\\ /       /4*pi\        /4*pi\\ /         /4*pi\      /4*pi\\ /           /4*pi\      /4*pi\\ /       /13*pi\        /13*pi\\ /       /13*pi\        /13*pi\\ /         /13*pi\      /13*pi\\ /           /13*pi\      /13*pi\\
(x + 1)*x*(x - 1)*|x + - + -------|*|x + - - -------|*|x + - - + -------|*|x + - - - -------|*|x + cos|--| + I*sin|--||*|x + cos|--| - I*sin|--||*|x + I*sin|--| - cos|--||*|x + - I*sin|--| - cos|--||*|x + cos|----| + I*sin|----||*|x + cos|----| - I*sin|----||*|x + I*sin|----| - cos|----||*|x + - I*sin|----| - cos|----||*|x + cos|--| + I*sin|--||*|x + cos|--| - I*sin|--||*|x + I*sin|--| - cos|--||*|x + - I*sin|--| - cos|--||*|x + cos|----| + I*sin|----||*|x + cos|----| - I*sin|----||*|x + I*sin|----| - cos|----||*|x + - I*sin|----| - cos|----||*|x + cos|----| + I*sin|----||*|x + cos|----| - I*sin|----||*|x + I*sin|----| - cos|----||*|x + - I*sin|----| - cos|----||*|x + cos|----| + I*sin|----||*|x + cos|----| - I*sin|----||*|x + I*sin|----| - cos|----||*|x + - I*sin|----| - cos|----||*|x + cos|----| + I*sin|----||*|x + cos|----| - I*sin|----||*|x + I*sin|----| - cos|----||*|x + - I*sin|----| - cos|----||*|x + cos|----| + I*sin|----||*|x + cos|----| - I*sin|----||*|x + I*sin|----| - cos|----||*|x + - I*sin|----| - cos|----||*|x + cos|-----| + I*sin|-----||*|x + cos|-----| - I*sin|-----||*|x + I*sin|-----| - cos|-----||*|x + - I*sin|-----| - cos|-----||*|x + cos|-----| + I*sin|-----||*|x + cos|-----| - I*sin|-----||*|x + I*sin|-----| - cos|-----||*|x + - I*sin|-----| - cos|-----||*|x + cos|----| + I*sin|----||*|x + cos|----| - I*sin|----||*|x + I*sin|----| - cos|----||*|x + - I*sin|----| - cos|----||*|x + cos|-----| + I*sin|-----||*|x + cos|-----| - I*sin|-----||*|x + I*sin|-----| - cos|-----||*|x + - I*sin|-----| - cos|-----||
                  \    2      2   / \    2      2   / \      2      2   / \      2      2   / \       \27/        \27// \       \27/        \27// \         \27/      \27// \           \27/      \27// \       \ 27 /        \ 27 // \       \ 27 /        \ 27 // \         \ 27 /      \ 27 // \           \ 27 /      \ 27 // \       \9 /        \9 // \       \9 /        \9 // \         \9 /      \9 // \           \9 /      \9 // \       \ 27 /        \ 27 // \       \ 27 /        \ 27 // \         \ 27 /      \ 27 // \           \ 27 /      \ 27 // \       \ 27 /        \ 27 // \       \ 27 /        \ 27 // \         \ 27 /      \ 27 // \           \ 27 /      \ 27 // \       \ 9  /        \ 9  // \       \ 9  /        \ 9  // \         \ 9  /      \ 9  // \           \ 9  /      \ 9  // \       \ 27 /        \ 27 // \       \ 27 /        \ 27 // \         \ 27 /      \ 27 // \           \ 27 /      \ 27 // \       \ 27 /        \ 27 // \       \ 27 /        \ 27 // \         \ 27 /      \ 27 // \           \ 27 /      \ 27 // \       \  27 /        \  27 // \       \  27 /        \  27 // \         \  27 /      \  27 // \           \  27 /      \  27 // \       \  27 /        \  27 // \       \  27 /        \  27 // \         \  27 /      \  27 // \           \  27 /      \  27 // \       \ 9  /        \ 9  // \       \ 9  /        \ 9  // \         \ 9  /      \ 9  // \           \ 9  /      \ 9  // \       \  27 /        \  27 // \       \  27 /        \  27 // \         \  27 /      \  27 // \           \  27 /      \  27 //
x(x+1)(x−1)(x+(12+3i2))(x+(12−3i2))(x+(−12+3i2))(x+(−12−3i2))(x+(cos⁡(π27)+isin⁡(π27)))(x+(cos⁡(π27)−isin⁡(π27)))(x+(−cos⁡(π27)+isin⁡(π27)))(x+(−cos⁡(π27)−isin⁡(π27)))(x+(cos⁡(2π27)+isin⁡(2π27)))(x+(cos⁡(2π27)−isin⁡(2π27)))(x+(−cos⁡(2π27)+isin⁡(2π27)))(x+(−cos⁡(2π27)−isin⁡(2π27)))(x+(cos⁡(π9)+isin⁡(π9)))(x+(cos⁡(π9)−isin⁡(π9)))(x+(−cos⁡(π9)+isin⁡(π9)))(x+(−cos⁡(π9)−isin⁡(π9)))(x+(cos⁡(4π27)+isin⁡(4π27)))(x+(cos⁡(4π27)−isin⁡(4π27)))(x+(−cos⁡(4π27)+isin⁡(4π27)))(x+(−cos⁡(4π27)−isin⁡(4π27)))(x+(cos⁡(5π27)+isin⁡(5π27)))(x+(cos⁡(5π27)−isin⁡(5π27)))(x+(−cos⁡(5π27)+isin⁡(5π27)))(x+(−cos⁡(5π27)−isin⁡(5π27)))(x+(cos⁡(2π9)+isin⁡(2π9)))(x+(cos⁡(2π9)−isin⁡(2π9)))(x+(−cos⁡(2π9)+isin⁡(2π9)))(x+(−cos⁡(2π9)−isin⁡(2π9)))(x+(cos⁡(7π27)+isin⁡(7π27)))(x+(cos⁡(7π27)−isin⁡(7π27)))(x+(−cos⁡(7π27)+isin⁡(7π27)))(x+(−cos⁡(7π27)−isin⁡(7π27)))(x+(cos⁡(8π27)+isin⁡(8π27)))(x+(cos⁡(8π27)−isin⁡(8π27)))(x+(−cos⁡(8π27)+isin⁡(8π27)))(x+(−cos⁡(8π27)−isin⁡(8π27)))(x+(cos⁡(10π27)+isin⁡(10π27)))(x+(cos⁡(10π27)−isin⁡(10π27)))(x+(−cos⁡(10π27)+isin⁡(10π27)))(x+(−cos⁡(10π27)−isin⁡(10π27)))(x+(cos⁡(11π27)+isin⁡(11π27)))(x+(cos⁡(11π27)−isin⁡(11π27)))(x+(−cos⁡(11π27)+isin⁡(11π27)))(x+(−cos⁡(11π27)−isin⁡(11π27)))(x+(cos⁡(4π9)+isin⁡(4π9)))(x+(cos⁡(4π9)−isin⁡(4π9)))(x+(−cos⁡(4π9)+isin⁡(4π9)))(x+(−cos⁡(4π9)−isin⁡(4π9)))(x+(cos⁡(13π27)+isin⁡(13π27)))(x+(cos⁡(13π27)−isin⁡(13π27)))(x+(−cos⁡(13π27)+isin⁡(13π27)))(x+(−cos⁡(13π27)−isin⁡(13π27)))x \left(x + 1\right) \left(x - 1\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{3} i}{2}\right)\right) \left(x + \left(\frac{1}{2} - \frac{\sqrt{3} i}{2}\right)\right) \left(x + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)\right) \left(x + \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)\right) \left(x + \left(\cos{\left(\frac{\pi}{27} \right)} + i \sin{\left(\frac{\pi}{27} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{\pi}{27} \right)} - i \sin{\left(\frac{\pi}{27} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{\pi}{27} \right)} + i \sin{\left(\frac{\pi}{27} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{\pi}{27} \right)} - i \sin{\left(\frac{\pi}{27} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{2 \pi}{27} \right)} + i \sin{\left(\frac{2 \pi}{27} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{2 \pi}{27} \right)} - i \sin{\left(\frac{2 \pi}{27} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{2 \pi}{27} \right)} + i \sin{\left(\frac{2 \pi}{27} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{2 \pi}{27} \right)} - i \sin{\left(\frac{2 \pi}{27} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{\pi}{9} \right)} + i \sin{\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(- \cos{\left(\frac{\pi}{9} \right)} + i \sin{\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(\cos{\left(\frac{4 \pi}{27} \right)} + i \sin{\left(\frac{4 \pi}{27} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{4 \pi}{27} \right)} - i \sin{\left(\frac{4 \pi}{27} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{4 \pi}{27} \right)} + i \sin{\left(\frac{4 \pi}{27} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{4 \pi}{27} \right)} - i \sin{\left(\frac{4 \pi}{27} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{5 \pi}{27} \right)} + i \sin{\left(\frac{5 \pi}{27} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{5 \pi}{27} \right)} - i \sin{\left(\frac{5 \pi}{27} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{5 \pi}{27} \right)} + i \sin{\left(\frac{5 \pi}{27} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{5 \pi}{27} \right)} - i \sin{\left(\frac{5 \pi}{27} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{2 \pi}{9} \right)} + i \sin{\left(\frac{2 \pi}{9} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{2 \pi}{9} \right)} - i \sin{\left(\frac{2 \pi}{9} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{2 \pi}{9} \right)} + i \sin{\left(\frac{2 \pi}{9} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{2 \pi}{9} \right)} - i \sin{\left(\frac{2 \pi}{9} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{7 \pi}{27} \right)} + i \sin{\left(\frac{7 \pi}{27} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{7 \pi}{27} \right)} - i \sin{\left(\frac{7 \pi}{27} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{7 \pi}{27} \right)} + i \sin{\left(\frac{7 \pi}{27} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{7 \pi}{27} \right)} - i \sin{\left(\frac{7 \pi}{27} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{8 \pi}{27} \right)} + i \sin{\left(\frac{8 \pi}{27} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{8 \pi}{27} \right)} - i \sin{\left(\frac{8 \pi}{27} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{8 \pi}{27} \right)} + i \sin{\left(\frac{8 \pi}{27} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{8 \pi}{27} \right)} - i \sin{\left(\frac{8 \pi}{27} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{10 \pi}{27} \right)} + i \sin{\left(\frac{10 \pi}{27} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{10 \pi}{27} \right)} - i \sin{\left(\frac{10 \pi}{27} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{10 \pi}{27} \right)} + i \sin{\left(\frac{10 \pi}{27} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{10 \pi}{27} \right)} - i \sin{\left(\frac{10 \pi}{27} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{11 \pi}{27} \right)} + i \sin{\left(\frac{11 \pi}{27} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{11 \pi}{27} \right)} - i \sin{\left(\frac{11 \pi}{27} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{11 \pi}{27} \right)} + i \sin{\left(\frac{11 \pi}{27} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{11 \pi}{27} \right)} - i \sin{\left(\frac{11 \pi}{27} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{4 \pi}{9} \right)} + i \sin{\left(\frac{4 \pi}{9} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{4 \pi}{9} \right)} - i \sin{\left(\frac{4 \pi}{9} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{4 \pi}{9} \right)} + i \sin{\left(\frac{4 \pi}{9} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{4 \pi}{9} \right)} - i \sin{\left(\frac{4 \pi}{9} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{13 \pi}{27} \right)} + i \sin{\left(\frac{13 \pi}{27} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{13 \pi}{27} \right)} - i \sin{\left(\frac{13 \pi}{27} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{13 \pi}{27} \right)} + i \sin{\left(\frac{13 \pi}{27} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{13 \pi}{27} \right)} - i \sin{\left(\frac{13 \pi}{27} \right)}\right)\right) 
((((((((((((((((((((((((((((((((((((((((((((((((((((((x + 1)*x)*(x - 1))*(x + 1/2 + i*sqrt(3)/2))*(x + 1/2 - i*sqrt(3)/2))*(x - 1/2 + i*sqrt(3)/2))*(x - 1/2 - i*sqrt(3)/2))*(x + cos(pi/27) + i*sin(pi/27)))*(x + cos(pi/27) - i*sin(pi/27)))*(x + i*sin(pi/27) - cos(pi/27)))*(x - i*sin(pi/27) - cos(pi/27)))*(x + cos(2*pi/27) + i*sin(2*pi/27)))*(x + cos(2*pi/27) - i*sin(2*pi/27)))*(x + i*sin(2*pi/27) - cos(2*pi/27)))*(x - i*sin(2*pi/27) - cos(2*pi/27)))*(x + cos(pi/9) + i*sin(pi/9)))*(x + cos(pi/9) - i*sin(pi/9)))*(x + i*sin(pi/9) - cos(pi/9)))*(x - i*sin(pi/9) - cos(pi/9)))*(x + cos(4*pi/27) + i*sin(4*pi/27)))*(x + cos(4*pi/27) - i*sin(4*pi/27)))*(x + i*sin(4*pi/27) - cos(4*pi/27)))*(x - i*sin(4*pi/27) - cos(4*pi/27)))*(x + cos(5*pi/27) + i*sin(5*pi/27)))*(x + cos(5*pi/27) - i*sin(5*pi/27)))*(x + i*sin(5*pi/27) - cos(5*pi/27)))*(x - i*sin(5*pi/27) - cos(5*pi/27)))*(x + cos(2*pi/9) + i*sin(2*pi/9)))*(x + cos(2*pi/9) - i*sin(2*pi/9)))*(x + i*sin(2*pi/9) - cos(2*pi/9)))*(x - i*sin(2*pi/9) - cos(2*pi/9)))*(x + cos(7*pi/27) + i*sin(7*pi/27)))*(x + cos(7*pi/27) - i*sin(7*pi/27)))*(x + i*sin(7*pi/27) - cos(7*pi/27)))*(x - i*sin(7*pi/27) - cos(7*pi/27)))*(x + cos(8*pi/27) + i*sin(8*pi/27)))*(x + cos(8*pi/27) - i*sin(8*pi/27)))*(x + i*sin(8*pi/27) - cos(8*pi/27)))*(x - i*sin(8*pi/27) - cos(8*pi/27)))*(x + cos(10*pi/27) + i*sin(10*pi/27)))*(x + cos(10*pi/27) - i*sin(10*pi/27)))*(x + i*sin(10*pi/27) - cos(10*pi/27)))*(x - i*sin(10*pi/27) - cos(10*pi/27)))*(x + cos(11*pi/27) + i*sin(11*pi/27)))*(x + cos(11*pi/27) - i*sin(11*pi/27)))*(x + i*sin(11*pi/27) - cos(11*pi/27)))*(x - i*sin(11*pi/27) - cos(11*pi/27)))*(x + cos(4*pi/9) + i*sin(4*pi/9)))*(x + cos(4*pi/9) - i*sin(4*pi/9)))*(x + i*sin(4*pi/9) - cos(4*pi/9)))*(x - i*sin(4*pi/9) - cos(4*pi/9)))*(x + cos(13*pi/27) + i*sin(13*pi/27)))*(x + cos(13*pi/27) - i*sin(13*pi/27)))*(x + i*sin(13*pi/27) - cos(13*pi/27)))*(x - i*sin(13*pi/27) - cos(13*pi/27))
Respuesta numérica [src] 
x^6 - x^60
x^6 - x^60
Unión de expresiones racionales [src] 
 6 /     54\
x *\1 - x  /
x6(1−x54)x^{6} \left(1 - x^{54}\right) 
x^6*(1 - x^54)
Combinatoria [src] 
  6                  /         2\ /     2    \ /     3    6\ /     6    3\ /     9    18\ /     18    9\
-x *(1 + x)*(-1 + x)*\1 + x + x /*\1 + x  - x/*\1 + x  + x /*\1 + x  - x /*\1 + x  + x  /*\1 + x   - x /
−x6(x−1)(x+1)(x2−x+1)(x2+x+1)(x6−x3+1)(x6+x3+1)(x18−x9+1)(x18+x9+1)- x^{6} \left(x - 1\right) \left(x + 1\right) \left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right) \left(x^{6} - x^{3} + 1\right) \left(x^{6} + x^{3} + 1\right) \left(x^{18} - x^{9} + 1\right) \left(x^{18} + x^{9} + 1\right) 
-x^6*(1 + x)*(-1 + x)*(1 + x + x^2)*(1 + x^2 - x)*(1 + x^3 + x^6)*(1 + x^6 - x^3)*(1 + x^9 + x^18)*(1 + x^18 - x^9)
    © Sr Examen – Калькулятор