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

Expresión a simplificar:

Solución

Ha introducido [src]
 3          
x  - 3*x + 3
$$\left(x^{3} - 3 x\right) + 3$$
x^3 - 3*x + 3
Simplificación general [src]
     3      
3 + x  - 3*x
$$x^{3} - 3 x + 3$$
3 + x^3 - 3*x
Factorización [src]
/                                                _______________                \ /                                                _______________                \ /                                _______________\
|                                               /           ___  /          ___\| |                                               /           ___  /          ___\| |                               /           ___ |
|                                              /  81   27*\/ 5   |  1   I*\/ 3 || |                                              /  81   27*\/ 5   |  1   I*\/ 3 || |                              /  81   27*\/ 5  |
|                                           3 /   -- + -------- *|- - - -------|| |                                           3 /   -- + -------- *|- - + -------|| |                           3 /   -- + -------- |
|                     3                     \/    2       2      \  2      2   /| |                     3                     \/    2       2      \  2      2   /| |             3             \/    2       2     |
|x + ------------------------------------ + ------------------------------------|*|x + ------------------------------------ + ------------------------------------|*|x + -------------------- + --------------------|
|                         _______________                    3                  | |                         _______________                    3                  | |         _______________            3          |
|    /          ___\     /           ___                                        | |    /          ___\     /           ___                                        | |        /           ___                        |
|    |  1   I*\/ 3 |    /  81   27*\/ 5                                         | |    |  1   I*\/ 3 |    /  81   27*\/ 5                                         | |       /  81   27*\/ 5                         |
|    |- - - -------|*3 /   -- + --------                                        | |    |- - + -------|*3 /   -- + --------                                        | |    3 /   -- + --------                        |
\    \  2      2   / \/    2       2                                            / \    \  2      2   / \/    2       2                                            / \    \/    2       2                            /
$$\left(x + \left(\frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}{3} + \frac{3}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}\right)\right) \left(x + \left(\frac{3}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}{3}\right)\right) \left(x + \left(\frac{3}{\sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}{3}\right)\right)$$
((x + 3/((-1/2 - i*sqrt(3)/2)*(81/2 + 27*sqrt(5)/2)^(1/3)) + (81/2 + 27*sqrt(5)/2)^(1/3)*(-1/2 - i*sqrt(3)/2)/3)*(x + 3/((-1/2 + i*sqrt(3)/2)*(81/2 + 27*sqrt(5)/2)^(1/3)) + (81/2 + 27*sqrt(5)/2)^(1/3)*(-1/2 + i*sqrt(3)/2)/3))*(x + 3/(81/2 + 27*sqrt(5)/2)^(1/3) + (81/2 + 27*sqrt(5)/2)^(1/3)/3)
Denominador común [src]
     3      
3 + x  - 3*x
$$x^{3} - 3 x + 3$$
3 + x^3 - 3*x
Parte trigonométrica [src]
     3      
3 + x  - 3*x
$$x^{3} - 3 x + 3$$
3 + x^3 - 3*x
Unión de expresiones racionales [src]
      /      2\
3 + x*\-3 + x /
$$x \left(x^{2} - 3\right) + 3$$
3 + x*(-3 + x^2)
Respuesta numérica [src]
3.0 + x^3 - 3.0*x
3.0 + x^3 - 3.0*x
Compilar la expresión [src]
     3      
3 + x  - 3*x
$$x^{3} - 3 x + 3$$
3 + x^3 - 3*x
Denominador racional [src]
     3      
3 + x  - 3*x
$$x^{3} - 3 x + 3$$
3 + x^3 - 3*x
Potencias [src]
     3      
3 + x  - 3*x
$$x^{3} - 3 x + 3$$
3 + x^3 - 3*x
Combinatoria [src]
     3      
3 + x  - 3*x
$$x^{3} - 3 x + 3$$
3 + x^3 - 3*x