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Factorizar el polinomio x+x^2+x^4-2*x^3

Expresión a simplificar:

Solución

Ha introducido [src]
     2    4      3
x + x  + x  - 2*x 
$$- 2 x^{3} + \left(x^{4} + \left(x^{2} + x\right)\right)$$
x + x^2 + x^4 - 2*x^3
Simplificación general [src]
  /         3      2\
x*\1 + x + x  - 2*x /
$$x \left(x^{3} - 2 x^{2} + x + 1\right)$$
x*(1 + x + x^3 - 2*x^2)
Factorización [src]
  /                                                        _______________                \ /                                                        _______________                \ /                                        _______________\
  |                                                       /          ____  /          ___\| |                                                       /          ____  /          ___\| |                                       /          ____ |
  |                                                      /  29   3*\/ 93   |  1   I*\/ 3 || |                                                      /  29   3*\/ 93   |  1   I*\/ 3 || |                                      /  29   3*\/ 93  |
  |                                                   3 /   -- + -------- *|- - - -------|| |                                                   3 /   -- + -------- *|- - + -------|| |                                   3 /   -- + -------- |
  |      2                     1                      \/    2       2      \  2      2   /| |      2                     1                      \/    2       2      \  2      2   /| |      2             1              \/    2       2     |
x*|x + - - + -------------------------------------- + ------------------------------------|*|x + - - + -------------------------------------- + ------------------------------------|*|x + - - + ---------------------- + --------------------|
  |      3                          _______________                    3                  | |      3                          _______________                    3                  | |      3          _______________            3          |
  |            /          ___\     /          ____                                        | |            /          ___\     /          ____                                        | |                /          ____                        |
  |            |  1   I*\/ 3 |    /  29   3*\/ 93                                         | |            |  1   I*\/ 3 |    /  29   3*\/ 93                                         | |               /  29   3*\/ 93                         |
  |          3*|- - - -------|*3 /   -- + --------                                        | |          3*|- - + -------|*3 /   -- + --------                                        | |          3*3 /   -- + --------                        |
  \            \  2      2   / \/    2       2                                            / \            \  2      2   / \/    2       2                                            / \            \/    2       2                            /
$$x \left(x + \left(- \frac{2}{3} + \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{2} + \frac{29}{2}}}{3} + \frac{1}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{2} + \frac{29}{2}}}\right)\right) \left(x + \left(- \frac{2}{3} + \frac{1}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{2} + \frac{29}{2}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{93}}{2} + \frac{29}{2}}}{3}\right)\right) \left(x + \left(- \frac{2}{3} + \frac{1}{3 \sqrt[3]{\frac{3 \sqrt{93}}{2} + \frac{29}{2}}} + \frac{\sqrt[3]{\frac{3 \sqrt{93}}{2} + \frac{29}{2}}}{3}\right)\right)$$
((x*(x - 2/3 + 1/(3*(-1/2 - i*sqrt(3)/2)*(29/2 + 3*sqrt(93)/2)^(1/3)) + (29/2 + 3*sqrt(93)/2)^(1/3)*(-1/2 - i*sqrt(3)/2)/3))*(x - 2/3 + 1/(3*(-1/2 + i*sqrt(3)/2)*(29/2 + 3*sqrt(93)/2)^(1/3)) + (29/2 + 3*sqrt(93)/2)^(1/3)*(-1/2 + i*sqrt(3)/2)/3))*(x - 2/3 + 1/(3*(29/2 + 3*sqrt(93)/2)^(1/3)) + (29/2 + 3*sqrt(93)/2)^(1/3)/3)
Respuesta numérica [src]
x + x^2 + x^4 - 2.0*x^3
x + x^2 + x^4 - 2.0*x^3
Parte trigonométrica [src]
     2    4      3
x + x  + x  - 2*x 
$$x^{4} - 2 x^{3} + x^{2} + x$$
x + x^2 + x^4 - 2*x^3
Potencias [src]
     2    4      3
x + x  + x  - 2*x 
$$x^{4} - 2 x^{3} + x^{2} + x$$
x + x^2 + x^4 - 2*x^3
Combinatoria [src]
  /         3      2\
x*\1 + x + x  - 2*x /
$$x \left(x^{3} - 2 x^{2} + x + 1\right)$$
x*(1 + x + x^3 - 2*x^2)
Unión de expresiones racionales [src]
  /         3      2\
x*\1 + x + x  - 2*x /
$$x \left(x^{3} - 2 x^{2} + x + 1\right)$$
x*(1 + x + x^3 - 2*x^2)
Denominador común [src]
     2    4      3
x + x  + x  - 2*x 
$$x^{4} - 2 x^{3} + x^{2} + x$$
x + x^2 + x^4 - 2*x^3
Compilar la expresión [src]
     2    4      3
x + x  + x  - 2*x 
$$x^{4} - 2 x^{3} + x^{2} + x$$
x + x^2 + x^4 - 2*x^3
Denominador racional [src]
     2    4      3
x + x  + x  - 2*x 
$$x^{4} - 2 x^{3} + x^{2} + x$$
x + x^2 + x^4 - 2*x^3