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Simplificación de expresiones/ Descomposición de multiplicadores/ x^5+x^4+x^3-x^2-x-1

Factorizar el polinomio x^5+x^4+x^3-x^2-x-1

Expresión a simplificar:

Solución

Ha introducido [src] 
 5    4    3    2        
x  + x  + x  - x  - x - 1
(−x+(−x2+(x3+(x5+x4))))−1\left(- x + \left(- x^{2} + \left(x^{3} + \left(x^{5} + x^{4}\right)\right)\right)\right) - 1 
x^5 + x^4 + x^3 - x^2 - x - 1
Factorización [src] 
        /            ___\ /            ___\
        |    1   I*\/ 3 | |    1   I*\/ 3 |
(x - 1)*|x + - + -------|*|x + - - -------|
        \    2      2   / \    2      2   /
(x−1)(x+(12+3i2))(x+(12−3i2))\left(x - 1\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{3} i}{2}\right)\right) \left(x + \left(\frac{1}{2} - \frac{\sqrt{3} i}{2}\right)\right) 
((x - 1)*(x + 1/2 + i*sqrt(3)/2))*(x + 1/2 - i*sqrt(3)/2)
Simplificación general [src] 
      3    4    5        2
-1 + x  + x  + x  - x - x
x5+x4+x3−x2−x−1x^{5} + x^{4} + x^{3} - x^{2} - x - 1 
-1 + x^3 + x^4 + x^5 - x - x^2
Denominador común [src] 
      3    4    5        2
-1 + x  + x  + x  - x - x
x5+x4+x3−x2−x−1x^{5} + x^{4} + x^{3} - x^{2} - x - 1 
-1 + x^3 + x^4 + x^5 - x - x^2
Combinatoria [src] 
            2         
/         2\          
\1 + x + x / *(-1 + x)
(x−1)(x2+x+1)2\left(x - 1\right) \left(x^{2} + x + 1\right)^{2} 
(1 + x + x^2)^2*(-1 + x)
Potencias [src] 
      3    4    5        2
-1 + x  + x  + x  - x - x
x5+x4+x3−x2−x−1x^{5} + x^{4} + x^{3} - x^{2} - x - 1 
-1 + x^3 + x^4 + x^5 - x - x^2
Parte trigonométrica [src] 
      3    4    5        2
-1 + x  + x  + x  - x - x
x5+x4+x3−x2−x−1x^{5} + x^{4} + x^{3} - x^{2} - x - 1 
-1 + x^3 + x^4 + x^5 - x - x^2
Compilar la expresión [src] 
      3    4    5        2
-1 + x  + x  + x  - x - x
x5+x4+x3−x2−x−1x^{5} + x^{4} + x^{3} - x^{2} - x - 1 
-1 + x^3 + x^4 + x^5 - x - x^2
Respuesta numérica [src] 
-1.0 + x^3 + x^4 + x^5 - x - x^2
-1.0 + x^3 + x^4 + x^5 - x - x^2
Denominador racional [src] 
      3    4    5        2
-1 + x  + x  + x  - x - x
x5+x4+x3−x2−x−1x^{5} + x^{4} + x^{3} - x^{2} - x - 1 
-1 + x^3 + x^4 + x^5 - x - x^2
Unión de expresiones racionales [src] 
-1 + x*(-1 + x*(-1 + x*(1 + x*(1 + x))))
x(x(x(x(x+1)+1)−1)−1)−1x \left(x \left(x \left(x \left(x + 1\right) + 1\right) - 1\right) - 1\right) - 1 
-1 + x*(-1 + x*(-1 + x*(1 + x*(1 + x))))
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