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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
(x+(x3−x2))+1\left(x + \left(x^{3} - x^{2}\right)\right) + 1 
x^3 - x^2 + x + 1
Simplificación general [src] 
         3    2
1 + x + x  - x
x3−x2+x+1x^{3} - x^{2} + x + 1 
1 + x + x^3 - x^2
Factorización [src] 
/             _______________ /          ___\                                       \ /             _______________ /          ___\                                       \                                                      
|          3 /          ____  |  1   I*\/ 3 |                                       | |          3 /          ____  |  1   I*\/ 3 |                                       | /             _______________                       \
|          \/  17 + 3*\/ 33  *|- - - -------|                                       | |          \/  17 + 3*\/ 33  *|- - + -------|                                       | |          3 /          ____                        |
|      1                      \  2      2   /                    2                  | |      1                      \  2      2   /                    2                  | |      1   \/  17 + 3*\/ 33              2          |
|x + - - + ---------------------------------- - ------------------------------------|*|x + - - + ---------------------------------- - ------------------------------------|*|x + - - + ------------------ - --------------------|
|      3                   3                         _______________ /          ___\| |      3                   3                         _______________ /          ___\| |      3           3                 _______________|
|                                                 3 /          ____  |  1   I*\/ 3 || |                                                 3 /          ____  |  1   I*\/ 3 || |                                 3 /          ____ |
|                                               3*\/  17 + 3*\/ 33  *|- - - -------|| |                                               3*\/  17 + 3*\/ 33  *|- - + -------|| \                               3*\/  17 + 3*\/ 33  /
\                                                                    \  2      2   // \                                                                    \  2      2   //
(x+(−13+(−12−3i2)17+33333−23(−12−3i2)17+3333))(x+(−13−23(−12+3i2)17+3333+(−12+3i2)17+33333))(x+(−13−2317+3333+17+33333))\left(x + \left(- \frac{1}{3} + \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{17 + 3 \sqrt{33}}}{3} - \frac{2}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{17 + 3 \sqrt{33}}}\right)\right) \left(x + \left(- \frac{1}{3} - \frac{2}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{17 + 3 \sqrt{33}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{17 + 3 \sqrt{33}}}{3}\right)\right) \left(x + \left(- \frac{1}{3} - \frac{2}{3 \sqrt[3]{17 + 3 \sqrt{33}}} + \frac{\sqrt[3]{17 + 3 \sqrt{33}}}{3}\right)\right) 
((x - 1/3 + (17 + 3*sqrt(33))^(1/3)*(-1/2 - i*sqrt(3)/2)/3 - 2/(3*(17 + 3*sqrt(33))^(1/3)*(-1/2 - i*sqrt(3)/2)))*(x - 1/3 + (17 + 3*sqrt(33))^(1/3)*(-1/2 + i*sqrt(3)/2)/3 - 2/(3*(17 + 3*sqrt(33))^(1/3)*(-1/2 + i*sqrt(3)/2))))*(x - 1/3 + (17 + 3*sqrt(33))^(1/3)/3 - 2/(3*(17 + 3*sqrt(33))^(1/3)))
Denominador común [src] 
         3    2
1 + x + x  - x
x3−x2+x+1x^{3} - x^{2} + x + 1 
1 + x + x^3 - x^2
Denominador racional [src] 
         3    2
1 + x + x  - x
x3−x2+x+1x^{3} - x^{2} + x + 1 
1 + x + x^3 - x^2
Combinatoria [src] 
         3    2
1 + x + x  - x
x3−x2+x+1x^{3} - x^{2} + x + 1 
1 + x + x^3 - x^2
Compilar la expresión [src] 
         3    2
1 + x + x  - x
x3−x2+x+1x^{3} - x^{2} + x + 1 
1 + x + x^3 - x^2
Parte trigonométrica [src] 
         3    2
1 + x + x  - x
x3−x2+x+1x^{3} - x^{2} + x + 1 
1 + x + x^3 - x^2
Potencias [src] 
         3    2
1 + x + x  - x
x3−x2+x+1x^{3} - x^{2} + x + 1 
1 + x + x^3 - x^2
Unión de expresiones racionales [src] 
1 + x*(1 + x*(-1 + x))
x(x(x−1)+1)+1x \left(x \left(x - 1\right) + 1\right) + 1 
1 + x*(1 + x*(-1 + x))
Respuesta numérica [src] 
1.0 + x + x^3 - x^2
1.0 + x + x^3 - x^2
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