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Simplificación de expresiones/ Descomposición de multiplicadores/ x^5-15*x^4+85*x^3-225*x^2-274*x+120

Factorizar el polinomio x^5-15*x^4+85*x^3-225*x^2-274*x+120

Expresión a simplificar:

Solución

Ha introducido [src] 
 5       4       3        2              
x  - 15*x  + 85*x  - 225*x  - 274*x + 120
$$\left(- 274 x + \left(- 225 x^{2} + \left(85 x^{3} + \left(x^{5} - 15 x^{4}\right)\right)\right)\right) + 120$$ 
x^5 - 15*x^4 + 85*x^3 - 225*x^2 - 274*x + 120
Simplificación general [src] 
       5                2       4       3
120 + x  - 274*x - 225*x  - 15*x  + 85*x
$$x^{5} - 15 x^{4} + 85 x^{3} - 225 x^{2} - 274 x + 120$$ 
120 + x^5 - 274*x - 225*x^2 - 15*x^4 + 85*x^3
Factorización [src] 
/           / 5       4       3        2                 \\ /           / 5       4       3        2                 \\ /           / 5       4       3        2                 \\ /           / 5       4       3        2                 \\ /           / 5       4       3        2                 \\
\x - CRootOf\x  - 15*x  + 85*x  - 225*x  - 274*x + 120, 0//*\x - CRootOf\x  - 15*x  + 85*x  - 225*x  - 274*x + 120, 1//*\x - CRootOf\x  - 15*x  + 85*x  - 225*x  - 274*x + 120, 2//*\x - CRootOf\x  - 15*x  + 85*x  - 225*x  - 274*x + 120, 3//*\x - CRootOf\x  - 15*x  + 85*x  - 225*x  - 274*x + 120, 4//
$$\left(x - \operatorname{CRootOf} {\left(x^{5} - 15 x^{4} + 85 x^{3} - 225 x^{2} - 274 x + 120, 0\right)}\right) \left(x - \operatorname{CRootOf} {\left(x^{5} - 15 x^{4} + 85 x^{3} - 225 x^{2} - 274 x + 120, 1\right)}\right) \left(x - \operatorname{CRootOf} {\left(x^{5} - 15 x^{4} + 85 x^{3} - 225 x^{2} - 274 x + 120, 2\right)}\right) \left(x - \operatorname{CRootOf} {\left(x^{5} - 15 x^{4} + 85 x^{3} - 225 x^{2} - 274 x + 120, 3\right)}\right) \left(x - \operatorname{CRootOf} {\left(x^{5} - 15 x^{4} + 85 x^{3} - 225 x^{2} - 274 x + 120, 4\right)}\right)$$ 
((((x - CRootOf(x^5 - 15*x^4 + 85*x^3 - 225*x^2 - 274*x + 120, 0))*(x - CRootOf(x^5 - 15*x^4 + 85*x^3 - 225*x^2 - 274*x + 120, 1)))*(x - CRootOf(x^5 - 15*x^4 + 85*x^3 - 225*x^2 - 274*x + 120, 2)))*(x - CRootOf(x^5 - 15*x^4 + 85*x^3 - 225*x^2 - 274*x + 120, 3)))*(x - CRootOf(x^5 - 15*x^4 + 85*x^3 - 225*x^2 - 274*x + 120, 4))
Respuesta numérica [src] 
120.0 + x^5 + 85.0*x^3 - 15.0*x^4 - 274.0*x - 225.0*x^2
120.0 + x^5 + 85.0*x^3 - 15.0*x^4 - 274.0*x - 225.0*x^2
Denominador racional [src] 
       5                2       4       3
120 + x  - 274*x - 225*x  - 15*x  + 85*x
$$x^{5} - 15 x^{4} + 85 x^{3} - 225 x^{2} - 274 x + 120$$ 
120 + x^5 - 274*x - 225*x^2 - 15*x^4 + 85*x^3
Denominador común [src] 
       5                2       4       3
120 + x  - 274*x - 225*x  - 15*x  + 85*x
$$x^{5} - 15 x^{4} + 85 x^{3} - 225 x^{2} - 274 x + 120$$ 
120 + x^5 - 274*x - 225*x^2 - 15*x^4 + 85*x^3
Unión de expresiones racionales [src] 
120 + x*(-274 + x*(-225 + x*(85 + x*(-15 + x))))
$$x \left(x \left(x \left(x \left(x - 15\right) + 85\right) - 225\right) - 274\right) + 120$$ 
120 + x*(-274 + x*(-225 + x*(85 + x*(-15 + x))))
Potencias [src] 
       5                2       4       3
120 + x  - 274*x - 225*x  - 15*x  + 85*x
$$x^{5} - 15 x^{4} + 85 x^{3} - 225 x^{2} - 274 x + 120$$ 
120 + x^5 - 274*x - 225*x^2 - 15*x^4 + 85*x^3
Combinatoria [src] 
       5                2       4       3
120 + x  - 274*x - 225*x  - 15*x  + 85*x
$$x^{5} - 15 x^{4} + 85 x^{3} - 225 x^{2} - 274 x + 120$$ 
120 + x^5 - 274*x - 225*x^2 - 15*x^4 + 85*x^3
Compilar la expresión [src] 
       5                2       4       3
120 + x  - 274*x - 225*x  - 15*x  + 85*x
$$x^{5} - 15 x^{4} + 85 x^{3} - 225 x^{2} - 274 x + 120$$ 
120 + x^5 - 274*x - 225*x^2 - 15*x^4 + 85*x^3
Parte trigonométrica [src] 
       5                2       4       3
120 + x  - 274*x - 225*x  - 15*x  + 85*x
$$x^{5} - 15 x^{4} + 85 x^{3} - 225 x^{2} - 274 x + 120$$ 
120 + x^5 - 274*x - 225*x^2 - 15*x^4 + 85*x^3
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