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Simplificación de expresiones/ Descomposición de multiplicadores/ x^5-x^4-x^3-x^2-x-2

Factorizar el polinomio x^5-x^4-x^3-x^2-x-2

Expresión a simplificar:

Solución

Ha introducido [src] 
 5    4    3    2        
x  - x  - x  - x  - x - 2
(−x+(−x2+(−x3+(x5−x4))))−2\left(- x + \left(- x^{2} + \left(- x^{3} + \left(x^{5} - x^{4}\right)\right)\right)\right) - 2 
x^5 - x^4 - x^3 - x^2 - x - 2
Simplificación general [src] 
      5        2    3    4
-2 + x  - x - x  - x  - x
x5−x4−x3−x2−x−2x^{5} - x^{4} - x^{3} - x^{2} - x - 2 
-2 + x^5 - x - x^2 - x^3 - x^4
Factorización [src] 
        /                       ___________\ /                       ___________\ /                       ___________\ /                       ___________\
        |          ___         /       ___ | |          ___         /       ___ | |          ___         /       ___ | |          ___         /       ___ |
        |    1   \/ 5         /  5   \/ 5  | |    1   \/ 5         /  5   \/ 5  | |    1   \/ 5         /  5   \/ 5  | |    1   \/ 5         /  5   \/ 5  |
(x - 2)*|x + - - ----- + I*  /   - + ----- |*|x + - - ----- - I*  /   - + ----- |*|x + - + ----- + I*  /   - - ----- |*|x + - + ----- - I*  /   - - ----- |
        \    4     4       \/    8     8   / \    4     4       \/    8     8   / \    4     4       \/    8     8   / \    4     4       \/    8     8   /
(x−2)(x+(−54+14+i58+58))(x+(−54+14−i58+58))(x+(14+54+i58−58))(x+(14+54−i58−58))\left(x - 2\right) \left(x + \left(- \frac{\sqrt{5}}{4} + \frac{1}{4} + i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(x + \left(- \frac{\sqrt{5}}{4} + \frac{1}{4} - i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(x + \left(\frac{1}{4} + \frac{\sqrt{5}}{4} + i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(x + \left(\frac{1}{4} + \frac{\sqrt{5}}{4} - i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) 
((((x - 2)*(x + 1/4 - sqrt(5)/4 + i*sqrt(5/8 + sqrt(5)/8)))*(x + 1/4 - sqrt(5)/4 - i*sqrt(5/8 + sqrt(5)/8)))*(x + 1/4 + sqrt(5)/4 + i*sqrt(5/8 - sqrt(5)/8)))*(x + 1/4 + sqrt(5)/4 - i*sqrt(5/8 - sqrt(5)/8))
Respuesta numérica [src] 
-2.0 + x^5 - x - x^2 - x^3 - x^4
-2.0 + x^5 - x - x^2 - x^3 - x^4
Unión de expresiones racionales [src] 
-2 + x*(-1 + x*(-1 + x*(-1 + x*(-1 + x))))
x(x(x(x(x−1)−1)−1)−1)−2x \left(x \left(x \left(x \left(x - 1\right) - 1\right) - 1\right) - 1\right) - 2 
-2 + x*(-1 + x*(-1 + x*(-1 + x*(-1 + x))))
Combinatoria [src] 
         /         2    3    4\
(-2 + x)*\1 + x + x  + x  + x /
(x−2)(x4+x3+x2+x+1)\left(x - 2\right) \left(x^{4} + x^{3} + x^{2} + x + 1\right) 
(-2 + x)*(1 + x + x^2 + x^3 + x^4)
Parte trigonométrica [src] 
      5        2    3    4
-2 + x  - x - x  - x  - x
x5−x4−x3−x2−x−2x^{5} - x^{4} - x^{3} - x^{2} - x - 2 
-2 + x^5 - x - x^2 - x^3 - x^4
Potencias [src] 
      5        2    3    4
-2 + x  - x - x  - x  - x
x5−x4−x3−x2−x−2x^{5} - x^{4} - x^{3} - x^{2} - x - 2 
-2 + x^5 - x - x^2 - x^3 - x^4
Compilar la expresión [src] 
      5        2    3    4
-2 + x  - x - x  - x  - x
x5−x4−x3−x2−x−2x^{5} - x^{4} - x^{3} - x^{2} - x - 2 
-2 + x^5 - x - x^2 - x^3 - x^4
Denominador racional [src] 
      5        2    3    4
-2 + x  - x - x  - x  - x
x5−x4−x3−x2−x−2x^{5} - x^{4} - x^{3} - x^{2} - x - 2 
-2 + x^5 - x - x^2 - x^3 - x^4
Denominador común [src] 
      5        2    3    4
-2 + x  - x - x  - x  - x
x5−x4−x3−x2−x−2x^{5} - x^{4} - x^{3} - x^{2} - x - 2 
-2 + x^5 - x - x^2 - x^3 - x^4
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