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Factorizar el polinomio x^3-x^2-x+20

Expresión a simplificar:

Solución

Ha introducido [src]
 3    2         
x  - x  - x + 20
$$\left(- x + \left(x^{3} - x^{2}\right)\right) + 20$$
x^3 - x^2 - x + 20
Simplificación general [src]
      3        2
20 + x  - x - x 
$$x^{3} - x^{2} - x + 20$$
20 + x^3 - x - x^2
Factorización [src]
/                                                            ___________________                \ /                                                            ___________________                \ /                                            ___________________\
|                                                           /           _______  /          ___\| |                                                           /           _______  /          ___\| |                                           /           _______ |
|                                                          /  529   3*\/ 31065   |  1   I*\/ 3 || |                                                          /  529   3*\/ 31065   |  1   I*\/ 3 || |                                          /  529   3*\/ 31065  |
|                                                       3 /   --- + ----------- *|- - - -------|| |                                                       3 /   --- + ----------- *|- - + -------|| |                                       3 /   --- + ----------- |
|      1                       4                        \/     2         2       \  2      2   /| |      1                       4                        \/     2         2       \  2      2   /| |      1               4                \/     2         2      |
|x + - - + ------------------------------------------ + ----------------------------------------|*|x + - - + ------------------------------------------ + ----------------------------------------|*|x + - - + -------------------------- + ------------------------|
|      3                          ___________________                      3                    | |      3                          ___________________                      3                    | |      3          ___________________              3            |
|            /          ___\     /           _______                                            | |            /          ___\     /           _______                                            | |                /           _______                            |
|            |  1   I*\/ 3 |    /  529   3*\/ 31065                                             | |            |  1   I*\/ 3 |    /  529   3*\/ 31065                                             | |               /  529   3*\/ 31065                             |
|          3*|- - - -------|*3 /   --- + -----------                                            | |          3*|- - + -------|*3 /   --- + -----------                                            | |          3*3 /   --- + -----------                            |
\            \  2      2   / \/     2         2                                                 / \            \  2      2   / \/     2         2                                                 / \            \/     2         2                                 /
$$\left(x + \left(- \frac{1}{3} + \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{31065}}{2} + \frac{529}{2}}}{3} + \frac{4}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{31065}}{2} + \frac{529}{2}}}\right)\right) \left(x + \left(- \frac{1}{3} + \frac{4}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{31065}}{2} + \frac{529}{2}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{31065}}{2} + \frac{529}{2}}}{3}\right)\right) \left(x + \left(- \frac{1}{3} + \frac{4}{3 \sqrt[3]{\frac{3 \sqrt{31065}}{2} + \frac{529}{2}}} + \frac{\sqrt[3]{\frac{3 \sqrt{31065}}{2} + \frac{529}{2}}}{3}\right)\right)$$
((x - 1/3 + 4/(3*(-1/2 - i*sqrt(3)/2)*(529/2 + 3*sqrt(31065)/2)^(1/3)) + (529/2 + 3*sqrt(31065)/2)^(1/3)*(-1/2 - i*sqrt(3)/2)/3)*(x - 1/3 + 4/(3*(-1/2 + i*sqrt(3)/2)*(529/2 + 3*sqrt(31065)/2)^(1/3)) + (529/2 + 3*sqrt(31065)/2)^(1/3)*(-1/2 + i*sqrt(3)/2)/3))*(x - 1/3 + 4/(3*(529/2 + 3*sqrt(31065)/2)^(1/3)) + (529/2 + 3*sqrt(31065)/2)^(1/3)/3)
Respuesta numérica [src]
20.0 + x^3 - x - x^2
20.0 + x^3 - x - x^2
Denominador racional [src]
      3        2
20 + x  - x - x 
$$x^{3} - x^{2} - x + 20$$
20 + x^3 - x - x^2
Combinatoria [src]
      3        2
20 + x  - x - x 
$$x^{3} - x^{2} - x + 20$$
20 + x^3 - x - x^2
Potencias [src]
      3        2
20 + x  - x - x 
$$x^{3} - x^{2} - x + 20$$
20 + x^3 - x - x^2
Denominador común [src]
      3        2
20 + x  - x - x 
$$x^{3} - x^{2} - x + 20$$
20 + x^3 - x - x^2
Unión de expresiones racionales [src]
20 + x*(-1 + x*(-1 + x))
$$x \left(x \left(x - 1\right) - 1\right) + 20$$
20 + x*(-1 + x*(-1 + x))
Compilar la expresión [src]
      3        2
20 + x  - x - x 
$$x^{3} - x^{2} - x + 20$$
20 + x^3 - x - x^2
Parte trigonométrica [src]
      3        2
20 + x  - x - x 
$$x^{3} - x^{2} - x + 20$$
20 + x^3 - x - x^2