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Simplificación de expresiones/ Descomposición de multiplicadores/ x^5-1

Factorizar el polinomio x^5-1

Expresión a simplificar:

Solución

Ha introducido [src] 
 5    
x  - 1
$$x^{5} - 1$$ 
x^5 - 1
Factorización [src] 
        /                       ___________\ /                       ___________\ /                       ___________\ /                       ___________\
        |          ___         /       ___ | |          ___         /       ___ | |          ___         /       ___ | |          ___         /       ___ |
        |    1   \/ 5         /  5   \/ 5  | |    1   \/ 5         /  5   \/ 5  | |    1   \/ 5         /  5   \/ 5  | |    1   \/ 5         /  5   \/ 5  |
(x - 1)*|x + - - ----- + I*  /   - + ----- |*|x + - - ----- - I*  /   - + ----- |*|x + - + ----- + I*  /   - - ----- |*|x + - + ----- - I*  /   - - ----- |
        \    4     4       \/    8     8   / \    4     4       \/    8     8   / \    4     4       \/    8     8   / \    4     4       \/    8     8   /
$$\left(x - 1\right) \left(x + \left(- \frac{\sqrt{5}}{4} + \frac{1}{4} + i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(x + \left(- \frac{\sqrt{5}}{4} + \frac{1}{4} - i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(x + \left(\frac{1}{4} + \frac{\sqrt{5}}{4} + i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(x + \left(\frac{1}{4} + \frac{\sqrt{5}}{4} - i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right)$$ 
((((x - 1)*(x + 1/4 - sqrt(5)/4 + i*sqrt(5/8 + sqrt(5)/8)))*(x + 1/4 - sqrt(5)/4 - i*sqrt(5/8 + sqrt(5)/8)))*(x + 1/4 + sqrt(5)/4 + i*sqrt(5/8 - sqrt(5)/8)))*(x + 1/4 + sqrt(5)/4 - i*sqrt(5/8 - sqrt(5)/8))
Respuesta numérica [src] 
-1.0 + x^5
-1.0 + x^5
Combinatoria [src] 
         /         2    3    4\
(-1 + x)*\1 + x + x  + x  + x /
$$\left(x - 1\right) \left(x^{4} + x^{3} + x^{2} + x + 1\right)$$ 
(-1 + x)*(1 + x + x^2 + x^3 + x^4)
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