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Factorizar el polinomio x^3-x+5

Expresión a simplificar:

Solución

Ha introducido [src]
 3        
x  - x + 5
$$\left(x^{3} - x\right) + 5$$
x^3 - x + 5
Factorización [src]
/                                                   __________________                \ /                                                   __________________                \ /                                   __________________\
|                                                  /           ______  /          ___\| |                                                  /           ______  /          ___\| |                                  /           ______ |
|                                                 /  135   3*\/ 2013   |  1   I*\/ 3 || |                                                 /  135   3*\/ 2013   |  1   I*\/ 3 || |                                 /  135   3*\/ 2013  |
|                                              3 /   --- + ---------- *|- - - -------|| |                                              3 /   --- + ---------- *|- - + -------|| |                              3 /   --- + ---------- |
|                       1                      \/     2        2       \  2      2   /| |                       1                      \/     2        2       \  2      2   /| |               1              \/     2        2      |
|x + --------------------------------------- + ---------------------------------------|*|x + --------------------------------------- + ---------------------------------------|*|x + ----------------------- + -----------------------|
|                         __________________                      3                   | |                         __________________                      3                   | |         __________________              3           |
|    /          ___\     /           ______                                           | |    /          ___\     /           ______                                           | |        /           ______                           |
|    |  1   I*\/ 3 |    /  135   3*\/ 2013                                            | |    |  1   I*\/ 3 |    /  135   3*\/ 2013                                            | |       /  135   3*\/ 2013                            |
|    |- - - -------|*3 /   --- + ----------                                           | |    |- - + -------|*3 /   --- + ----------                                           | |    3 /   --- + ----------                           |
\    \  2      2   / \/     2        2                                                / \    \  2      2   / \/     2        2                                                / \    \/     2        2                                /
$$\left(x + \left(\frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{2013}}{2} + \frac{135}{2}}}{3} + \frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{2013}}{2} + \frac{135}{2}}}\right)\right) \left(x + \left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{2013}}{2} + \frac{135}{2}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{2013}}{2} + \frac{135}{2}}}{3}\right)\right) \left(x + \left(\frac{1}{\sqrt[3]{\frac{3 \sqrt{2013}}{2} + \frac{135}{2}}} + \frac{\sqrt[3]{\frac{3 \sqrt{2013}}{2} + \frac{135}{2}}}{3}\right)\right)$$
((x + 1/((-1/2 - i*sqrt(3)/2)*(135/2 + 3*sqrt(2013)/2)^(1/3)) + (135/2 + 3*sqrt(2013)/2)^(1/3)*(-1/2 - i*sqrt(3)/2)/3)*(x + 1/((-1/2 + i*sqrt(3)/2)*(135/2 + 3*sqrt(2013)/2)^(1/3)) + (135/2 + 3*sqrt(2013)/2)^(1/3)*(-1/2 + i*sqrt(3)/2)/3))*(x + (135/2 + 3*sqrt(2013)/2)^(-1/3) + (135/2 + 3*sqrt(2013)/2)^(1/3)/3)
Simplificación general [src]
     3    
5 + x  - x
$$x^{3} - x + 5$$
5 + x^3 - x
Denominador racional [src]
     3    
5 + x  - x
$$x^{3} - x + 5$$
5 + x^3 - x
Parte trigonométrica [src]
     3    
5 + x  - x
$$x^{3} - x + 5$$
5 + x^3 - x
Compilar la expresión [src]
     3    
5 + x  - x
$$x^{3} - x + 5$$
5 + x^3 - x
Combinatoria [src]
     3    
5 + x  - x
$$x^{3} - x + 5$$
5 + x^3 - x
Denominador común [src]
     3    
5 + x  - x
$$x^{3} - x + 5$$
5 + x^3 - x
Respuesta numérica [src]
5.0 + x^3 - x
5.0 + x^3 - x
Unión de expresiones racionales [src]
      /      2\
5 + x*\-1 + x /
$$x \left(x^{2} - 1\right) + 5$$
5 + x*(-1 + x^2)
Potencias [src]
     3    
5 + x  - x
$$x^{3} - x + 5$$
5 + x^3 - x