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Simplificación de expresiones/ Descomposición de multiplicadores/ x^3+x^2+x-2

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

Expresión a simplificar:

Solución

Ha introducido [src] 
 3    2        
x  + x  + x - 2
$$\left(x + \left(x^{3} + x^{2}\right)\right) - 2$$ 
x^3 + x^2 + x - 2
Simplificación general [src] 
          2    3
-2 + x + x  + x
$$x^{3} + x^{2} + x - 2$$ 
-2 + x + x^2 + x^3
Factorización [src] 
/             ______________                                                        \ /             ______________                                                        \ /             ______________                        \
|            /        _____  /          ___\                                        | |            /        _____  /          ___\                                        | |            /        _____                         |
|    1      /  61   \/ 417   |  1   I*\/ 3 |                     2                  | |    1      /  61   \/ 417   |  1   I*\/ 3 |                     2                  | |    1      /  61   \/ 417               2          |
|x + - - 3 /   -- + ------- *|- - - -------| + -------------------------------------|*|x + - - 3 /   -- + ------- *|- - + -------| + -------------------------------------|*|x + - - 3 /   -- + -------  + ---------------------|
|    3   \/    54      18    \  2      2   /                          ______________| |    3   \/    54      18    \  2      2   /                          ______________| |    3   \/    54      18             ______________|
|                                                /          ___\     /        _____ | |                                                /          ___\     /        _____ | |                                    /        _____ |
|                                                |  1   I*\/ 3 |    /  61   \/ 417  | |                                                |  1   I*\/ 3 |    /  61   \/ 417  | |                                   /  61   \/ 417  |
|                                              9*|- - - -------|*3 /   -- + ------- | |                                              9*|- - + -------|*3 /   -- + ------- | |                              9*3 /   -- + ------- |
\                                                \  2      2   / \/    54      18   / \                                                \  2      2   / \/    54      18   / \                                \/    54      18   /
$$\left(x + \left(\frac{1}{3} + \frac{2}{9 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{61}{54} + \frac{\sqrt{417}}{18}}} - \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{61}{54} + \frac{\sqrt{417}}{18}}\right)\right) \left(x + \left(\frac{1}{3} - \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{61}{54} + \frac{\sqrt{417}}{18}} + \frac{2}{9 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{61}{54} + \frac{\sqrt{417}}{18}}}\right)\right) \left(x + \left(- \sqrt[3]{\frac{61}{54} + \frac{\sqrt{417}}{18}} + \frac{2}{9 \sqrt[3]{\frac{61}{54} + \frac{\sqrt{417}}{18}}} + \frac{1}{3}\right)\right)$$ 
((x + 1/3 - (61/54 + sqrt(417)/18)^(1/3)*(-1/2 - i*sqrt(3)/2) + 2/(9*(-1/2 - i*sqrt(3)/2)*(61/54 + sqrt(417)/18)^(1/3)))*(x + 1/3 - (61/54 + sqrt(417)/18)^(1/3)*(-1/2 + i*sqrt(3)/2) + 2/(9*(-1/2 + i*sqrt(3)/2)*(61/54 + sqrt(417)/18)^(1/3))))*(x + 1/3 - (61/54 + sqrt(417)/18)^(1/3) + 2/(9*(61/54 + sqrt(417)/18)^(1/3)))
Denominador racional [src] 
          2    3
-2 + x + x  + x
$$x^{3} + x^{2} + x - 2$$ 
-2 + x + x^2 + x^3
Parte trigonométrica [src] 
          2    3
-2 + x + x  + x
$$x^{3} + x^{2} + x - 2$$ 
-2 + x + x^2 + x^3
Combinatoria [src] 
          2    3
-2 + x + x  + x
$$x^{3} + x^{2} + x - 2$$ 
-2 + x + x^2 + x^3
Potencias [src] 
          2    3
-2 + x + x  + x
$$x^{3} + x^{2} + x - 2$$ 
-2 + x + x^2 + x^3
Unión de expresiones racionales [src] 
-2 + x*(1 + x*(1 + x))
$$x \left(x \left(x + 1\right) + 1\right) - 2$$ 
-2 + x*(1 + x*(1 + x))
Respuesta numérica [src] 
-2.0 + x + x^2 + x^3
-2.0 + x + x^2 + x^3
Denominador común [src] 
          2    3
-2 + x + x  + x
$$x^{3} + x^{2} + x - 2$$ 
-2 + x + x^2 + x^3
Compilar la expresión [src] 
          2    3
-2 + x + x  + x
$$x^{3} + x^{2} + x - 2$$ 
-2 + x + x^2 + x^3
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