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Simplificación de expresiones/ Descomposición de multiplicadores/ x^3+x^2+x-1

Factorizar el polinomio x^3+x^2+x-1

Expresión a simplificar:

Solución

Ha introducido [src] 
 3    2        
x  + x  + x - 1
$$\left(x + \left(x^{3} + x^{2}\right)\right) - 1$$ 
x^3 + x^2 + x - 1
Simplificación general [src] 
          2    3
-1 + x + x  + x
$$x^{3} + x^{2} + x - 1$$ 
-1 + x + x^2 + x^3
Factorización [src] 
/             _____________                                                       \ /             _____________                                                       \ /             _____________                       \
|            /        ____  /          ___\                                       | |            /        ____  /          ___\                                       | |            /        ____                        |
|    1      /  17   \/ 33   |  1   I*\/ 3 |                    2                  | |    1      /  17   \/ 33   |  1   I*\/ 3 |                    2                  | |    1      /  17   \/ 33              2          |
|x + - - 3 /   -- + ------ *|- - - -------| + ------------------------------------|*|x + - - 3 /   -- + ------ *|- - + -------| + ------------------------------------|*|x + - - 3 /   -- + ------  + --------------------|
|    3   \/    27     9     \  2      2   /                          _____________| |    3   \/    27     9     \  2      2   /                          _____________| |    3   \/    27     9              _____________|
|                                               /          ___\     /        ____ | |                                               /          ___\     /        ____ | |                                   /        ____ |
|                                               |  1   I*\/ 3 |    /  17   \/ 33  | |                                               |  1   I*\/ 3 |    /  17   \/ 33  | |                                  /  17   \/ 33  |
|                                             9*|- - - -------|*3 /   -- + ------ | |                                             9*|- - + -------|*3 /   -- + ------ | |                             9*3 /   -- + ------ |
\                                               \  2      2   / \/    27     9    / \                                               \  2      2   / \/    27     9    / \                               \/    27     9    /
$$\left(x + \left(\frac{1}{3} + \frac{2}{9 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}} - \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}\right)\right) \left(x + \left(\frac{1}{3} - \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}} + \frac{2}{9 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}}\right)\right) \left(x + \left(- \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}} + \frac{2}{9 \sqrt[3]{\frac{17}{27} + \frac{\sqrt{33}}{9}}} + \frac{1}{3}\right)\right)$$ 
((x + 1/3 - (17/27 + sqrt(33)/9)^(1/3)*(-1/2 - i*sqrt(3)/2) + 2/(9*(-1/2 - i*sqrt(3)/2)*(17/27 + sqrt(33)/9)^(1/3)))*(x + 1/3 - (17/27 + sqrt(33)/9)^(1/3)*(-1/2 + i*sqrt(3)/2) + 2/(9*(-1/2 + i*sqrt(3)/2)*(17/27 + sqrt(33)/9)^(1/3))))*(x + 1/3 - (17/27 + sqrt(33)/9)^(1/3) + 2/(9*(17/27 + sqrt(33)/9)^(1/3)))
Parte trigonométrica [src] 
          2    3
-1 + x + x  + x
$$x^{3} + x^{2} + x - 1$$ 
-1 + x + x^2 + x^3
Potencias [src] 
          2    3
-1 + x + x  + x
$$x^{3} + x^{2} + x - 1$$ 
-1 + x + x^2 + x^3
Compilar la expresión [src] 
          2    3
-1 + x + x  + x
$$x^{3} + x^{2} + x - 1$$ 
-1 + x + x^2 + x^3
Denominador racional [src] 
          2    3
-1 + x + x  + x
$$x^{3} + x^{2} + x - 1$$ 
-1 + x + x^2 + x^3
Respuesta numérica [src] 
-1.0 + x + x^2 + x^3
-1.0 + x + x^2 + x^3
Combinatoria [src] 
          2    3
-1 + x + x  + x
$$x^{3} + x^{2} + x - 1$$ 
-1 + x + x^2 + x^3
Denominador común [src] 
          2    3
-1 + x + x  + x
$$x^{3} + x^{2} + x - 1$$ 
-1 + x + x^2 + x^3
Unión de expresiones racionales [src] 
-1 + x*(1 + x*(1 + x))
$$x \left(x \left(x + 1\right) + 1\right) - 1$$ 
-1 + x*(1 + x*(1 + x))
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