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Simplificación de expresiones/ Descomposición de multiplicadores/ x^8-1

Factorizar el polinomio x^8-1

Expresión a simplificar:

Solución

Ha introducido [src] 
 8    
x  - 1
x8−1x^{8} - 1 
x^8 - 1
Factorización [src] 
                                /      ___       ___\ /      ___       ___\ /        ___       ___\ /        ___       ___\
                                |    \/ 2    I*\/ 2 | |    \/ 2    I*\/ 2 | |      \/ 2    I*\/ 2 | |      \/ 2    I*\/ 2 |
(x + 1)*(x - 1)*(x + I)*(x - I)*|x + ----- + -------|*|x + ----- - -------|*|x + - ----- + -------|*|x + - ----- - -------|
                                \      2        2   / \      2        2   / \        2        2   / \        2        2   /
(x−1)(x+1)(x+i)(x−i)(x+(22+2i2))(x+(22−2i2))(x+(−22+2i2))(x+(−22−2i2))\left(x - 1\right) \left(x + 1\right) \left(x + i\right) \left(x - i\right) \left(x + \left(\frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) \left(x + \left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right) \left(x + \left(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) \left(x + \left(- \frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right) 
(((((((x + 1)*(x - 1))*(x + i))*(x - i))*(x + sqrt(2)/2 + i*sqrt(2)/2))*(x + sqrt(2)/2 - i*sqrt(2)/2))*(x - sqrt(2)/2 + i*sqrt(2)/2))*(x - sqrt(2)/2 - i*sqrt(2)/2)
Respuesta numérica [src] 
-1.0 + x^8
-1.0 + x^8
Combinatoria [src] 
        /     2\ /     4\         
(1 + x)*\1 + x /*\1 + x /*(-1 + x)
(x−1)(x+1)(x2+1)(x4+1)\left(x - 1\right) \left(x + 1\right) \left(x^{2} + 1\right) \left(x^{4} + 1\right) 
(1 + x)*(1 + x^2)*(1 + x^4)*(-1 + x)
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