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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]
/             ________________                                                          \ /             ________________                                                          \ /             ________________                          \
|            /          _____  /          ___\                                          | |            /          _____  /          ___\                                          | |            /          _____                           |
|           /  47   3*\/ 249   |  1   I*\/ 3 |                                          | |           /  47   3*\/ 249   |  1   I*\/ 3 |                                          | |           /  47   3*\/ 249                            |
|        3 /   -- + --------- *|- - - -------|                                          | |        3 /   -- + --------- *|- - + -------|                                          | |        3 /   -- + ---------                           |
|    1   \/    2        2      \  2      2   /                      2                   | |    1   \/    2        2      \  2      2   /                      2                   | |    1   \/    2        2                   2           |
|x + - + ------------------------------------- - ---------------------------------------|*|x + - + ------------------------------------- - ---------------------------------------|*|x + - + --------------------- - -----------------------|
|    3                     3                                            ________________| |    3                     3                                            ________________| |    3             3                    ________________|
|                                                  /          ___\     /          _____ | |                                                  /          ___\     /          _____ | |                                      /          _____ |
|                                                  |  1   I*\/ 3 |    /  47   3*\/ 249  | |                                                  |  1   I*\/ 3 |    /  47   3*\/ 249  | |                                     /  47   3*\/ 249  |
|                                                3*|- - - -------|*3 /   -- + --------- | |                                                3*|- - + -------|*3 /   -- + --------- | |                                3*3 /   -- + --------- |
\                                                  \  2      2   / \/    2        2     / \                                                  \  2      2   / \/    2        2     / \                                  \/    2        2     /
$$\left(x + \left(\frac{1}{3} + \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{47}{2} + \frac{3 \sqrt{249}}{2}}}{3} - \frac{2}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{47}{2} + \frac{3 \sqrt{249}}{2}}}\right)\right) \left(x + \left(\frac{1}{3} - \frac{2}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{47}{2} + \frac{3 \sqrt{249}}{2}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{47}{2} + \frac{3 \sqrt{249}}{2}}}{3}\right)\right) \left(x + \left(- \frac{2}{3 \sqrt[3]{\frac{47}{2} + \frac{3 \sqrt{249}}{2}}} + \frac{1}{3} + \frac{\sqrt[3]{\frac{47}{2} + \frac{3 \sqrt{249}}{2}}}{3}\right)\right)$$
((x + 1/3 + (47/2 + 3*sqrt(249)/2)^(1/3)*(-1/2 - i*sqrt(3)/2)/3 - 2/(3*(-1/2 - i*sqrt(3)/2)*(47/2 + 3*sqrt(249)/2)^(1/3)))*(x + 1/3 + (47/2 + 3*sqrt(249)/2)^(1/3)*(-1/2 + i*sqrt(3)/2)/3 - 2/(3*(-1/2 + i*sqrt(3)/2)*(47/2 + 3*sqrt(249)/2)^(1/3))))*(x + 1/3 + (47/2 + 3*sqrt(249)/2)^(1/3)/3 - 2/(3*(47/2 + 3*sqrt(249)/2)^(1/3)))
Parte trigonométrica [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))
Denominador racional [src]
         2    3
2 + x + x  + x 
$$x^{3} + x^{2} + x + 2$$
2 + 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
Combinatoria [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
Respuesta numérica [src]
2.0 + x + x^2 + x^3
2.0 + x + x^2 + x^3