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Factorizar el polinomio x+x^5/5

Expresión a simplificar:

Solución

Ha introducido [src]
     5
    x 
x + --
    5 
$$\frac{x^{5}}{5} + x$$
x + x^5/5
Factorización [src]
  /      ___ 4 ___       ___ 4 ___\ /      ___ 4 ___       ___ 4 ___\ /        ___ 4 ___       ___ 4 ___\ /        ___ 4 ___       ___ 4 ___\
  |    \/ 2 *\/ 5    I*\/ 2 *\/ 5 | |    \/ 2 *\/ 5    I*\/ 2 *\/ 5 | |      \/ 2 *\/ 5    I*\/ 2 *\/ 5 | |      \/ 2 *\/ 5    I*\/ 2 *\/ 5 |
x*|x + ----------- + -------------|*|x + ----------- - -------------|*|x + - ----------- + -------------|*|x + - ----------- - -------------|
  \         2              2      / \         2              2      / \           2              2      / \           2              2      /
$$x \left(x + \left(\frac{\sqrt{2} \sqrt[4]{5}}{2} + \frac{\sqrt{2} \sqrt[4]{5} i}{2}\right)\right) \left(x + \left(\frac{\sqrt{2} \sqrt[4]{5}}{2} - \frac{\sqrt{2} \sqrt[4]{5} i}{2}\right)\right) \left(x + \left(- \frac{\sqrt{2} \sqrt[4]{5}}{2} + \frac{\sqrt{2} \sqrt[4]{5} i}{2}\right)\right) \left(x + \left(- \frac{\sqrt{2} \sqrt[4]{5}}{2} - \frac{\sqrt{2} \sqrt[4]{5} i}{2}\right)\right)$$
(((x*(x + sqrt(2)*5^(1/4)/2 + i*sqrt(2)*5^(1/4)/2))*(x + sqrt(2)*5^(1/4)/2 - i*sqrt(2)*5^(1/4)/2))*(x - sqrt(2)*5^(1/4)/2 + i*sqrt(2)*5^(1/4)/2))*(x - sqrt(2)*5^(1/4)/2 - i*sqrt(2)*5^(1/4)/2)
Descomposición de una fracción [src]
x + x^5/5
$$\frac{x^{5}}{5} + x$$
     5
    x 
x + --
    5 
Combinatoria [src]
  /     4\
x*\5 + x /
----------
    5     
$$\frac{x \left(x^{4} + 5\right)}{5}$$
x*(5 + x^4)/5
Denominador racional [src]
 5      
x  + 5*x
--------
   5    
$$\frac{x^{5} + 5 x}{5}$$
(x^5 + 5*x)/5
Respuesta numérica [src]
x + 0.2*x^5
x + 0.2*x^5
Unión de expresiones racionales [src]
  /     4\
x*\5 + x /
----------
    5     
$$\frac{x \left(x^{4} + 5\right)}{5}$$
x*(5 + x^4)/5