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Factorizar el polinomio x^3+x+1

Expresión a simplificar:

Solución

Ha introducido [src]
 3        
x  + x + 1
$$\left(x^{3} + x\right) + 1$$
x^3 + x + 1
Factorización [src]
/                                                  _______________                \ /                                                  _______________                \ /                                  _______________\
|                                                 /          ____  /          ___\| |                                                 /          ____  /          ___\| |                                 /          ____ |
|                                                /  27   3*\/ 93   |  1   I*\/ 3 || |                                                /  27   3*\/ 93   |  1   I*\/ 3 || |                                /  27   3*\/ 93  |
|                                             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 |    /  27   3*\/ 93                                         | |      |  1   I*\/ 3 |    /  27   3*\/ 93                                         | |         /  27   3*\/ 93                         |
|      |- - - -------|*3 /   -- + --------                                        | |      |- - + -------|*3 /   -- + --------                                        | |      3 /   -- + --------                        |
\      \  2      2   / \/    2       2                                            / \      \  2      2   / \/    2       2                                            / \      \/    2       2                            /
$$\left(x + \left(\frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{3 \sqrt{93}}{2}}}{3} - \frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{3 \sqrt{93}}{2}}}\right)\right) \left(x + \left(- \frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{3 \sqrt{93}}{2}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{3 \sqrt{93}}{2}}}{3}\right)\right) \left(x + \left(- \frac{1}{\sqrt[3]{\frac{27}{2} + \frac{3 \sqrt{93}}{2}}} + \frac{\sqrt[3]{\frac{27}{2} + \frac{3 \sqrt{93}}{2}}}{3}\right)\right)$$
((x - 1/((-1/2 - i*sqrt(3)/2)*(27/2 + 3*sqrt(93)/2)^(1/3)) + (27/2 + 3*sqrt(93)/2)^(1/3)*(-1/2 - i*sqrt(3)/2)/3)*(x - 1/((-1/2 + i*sqrt(3)/2)*(27/2 + 3*sqrt(93)/2)^(1/3)) + (27/2 + 3*sqrt(93)/2)^(1/3)*(-1/2 + i*sqrt(3)/2)/3))*(x - 1/(27/2 + 3*sqrt(93)/2)^(1/3) + (27/2 + 3*sqrt(93)/2)^(1/3)/3)
Simplificación general [src]
         3
1 + x + x 
$$x^{3} + x + 1$$
1 + x + x^3
Compilar la expresión [src]
         3
1 + x + x 
$$x^{3} + x + 1$$
1 + x + x^3
Denominador común [src]
         3
1 + x + x 
$$x^{3} + x + 1$$
1 + x + x^3
Respuesta numérica [src]
1.0 + x + x^3
1.0 + x + x^3
Unión de expresiones racionales [src]
      /     2\
1 + x*\1 + x /
$$x \left(x^{2} + 1\right) + 1$$
1 + x*(1 + x^2)
Parte trigonométrica [src]
         3
1 + x + x 
$$x^{3} + x + 1$$
1 + x + x^3
Potencias [src]
         3
1 + x + x 
$$x^{3} + x + 1$$
1 + x + x^3
Combinatoria [src]
         3
1 + x + x 
$$x^{3} + x + 1$$
1 + x + x^3
Denominador racional [src]
         3
1 + x + x 
$$x^{3} + x + 1$$
1 + x + x^3