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Factorizar el polinomio x^3-12*x+7

Expresión a simplificar:

Solución

Ha introducido [src]
 3           
x  - 12*x + 7
$$\left(x^{3} - 12 x\right) + 7$$
x^3 - 12*x + 7
Simplificación general [src]
     3       
7 + x  - 12*x
$$x^{3} - 12 x + 7$$
7 + x^3 - 12*x
Factorización [src]
/                                                    ___________________                \ /                                                    ___________________                \ /                                    ___________________\
|                                                   /              ____  /          ___\| |                                                   /              ____  /          ___\| |                                   /              ____ |
|                                                  /  189   81*I*\/ 23   |  1   I*\/ 3 || |                                                  /  189   81*I*\/ 23   |  1   I*\/ 3 || |                                  /  189   81*I*\/ 23  |
|                                               3 /   --- + ----------- *|- - - -------|| |                                               3 /   --- + ----------- *|- - + -------|| |                               3 /   --- + ----------- |
|                       12                      \/     2         2       \  2      2   /| |                       12                      \/     2         2       \  2      2   /| |               12              \/     2         2      |
|x + ---------------------------------------- + ----------------------------------------|*|x + ---------------------------------------- + ----------------------------------------|*|x + ------------------------ + ------------------------|
|                         ___________________                      3                    | |                         ___________________                      3                    | |         ___________________              3            |
|    /          ___\     /              ____                                            | |    /          ___\     /              ____                                            | |        /              ____                            |
|    |  1   I*\/ 3 |    /  189   81*I*\/ 23                                             | |    |  1   I*\/ 3 |    /  189   81*I*\/ 23                                             | |       /  189   81*I*\/ 23                             |
|    |- - - -------|*3 /   --- + -----------                                            | |    |- - + -------|*3 /   --- + -----------                                            | |    3 /   --- + -----------                            |
\    \  2      2   / \/     2         2                                                 / \    \  2      2   / \/     2         2                                                 / \    \/     2         2                                 /
$$\left(x + \left(\frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{189}{2} + \frac{81 \sqrt{23} i}{2}}}{3} + \frac{12}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{189}{2} + \frac{81 \sqrt{23} i}{2}}}\right)\right) \left(x + \left(\frac{12}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{189}{2} + \frac{81 \sqrt{23} i}{2}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{189}{2} + \frac{81 \sqrt{23} i}{2}}}{3}\right)\right) \left(x + \left(\frac{12}{\sqrt[3]{\frac{189}{2} + \frac{81 \sqrt{23} i}{2}}} + \frac{\sqrt[3]{\frac{189}{2} + \frac{81 \sqrt{23} i}{2}}}{3}\right)\right)$$
((x + 12/((-1/2 - i*sqrt(3)/2)*(189/2 + 81*i*sqrt(23)/2)^(1/3)) + (189/2 + 81*i*sqrt(23)/2)^(1/3)*(-1/2 - i*sqrt(3)/2)/3)*(x + 12/((-1/2 + i*sqrt(3)/2)*(189/2 + 81*i*sqrt(23)/2)^(1/3)) + (189/2 + 81*i*sqrt(23)/2)^(1/3)*(-1/2 + i*sqrt(3)/2)/3))*(x + 12/(189/2 + 81*i*sqrt(23)/2)^(1/3) + (189/2 + 81*i*sqrt(23)/2)^(1/3)/3)
Compilar la expresión [src]
     3       
7 + x  - 12*x
$$x^{3} - 12 x + 7$$
7 + x^3 - 12*x
Respuesta numérica [src]
7.0 + x^3 - 12.0*x
7.0 + x^3 - 12.0*x
Unión de expresiones racionales [src]
      /       2\
7 + x*\-12 + x /
$$x \left(x^{2} - 12\right) + 7$$
7 + x*(-12 + x^2)
Potencias [src]
     3       
7 + x  - 12*x
$$x^{3} - 12 x + 7$$
7 + x^3 - 12*x
Denominador racional [src]
     3       
7 + x  - 12*x
$$x^{3} - 12 x + 7$$
7 + x^3 - 12*x
Denominador común [src]
     3       
7 + x  - 12*x
$$x^{3} - 12 x + 7$$
7 + x^3 - 12*x
Combinatoria [src]
     3       
7 + x  - 12*x
$$x^{3} - 12 x + 7$$
7 + x^3 - 12*x
Parte trigonométrica [src]
     3       
7 + x  - 12*x
$$x^{3} - 12 x + 7$$
7 + x^3 - 12*x