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Simplificación de expresiones/ Descomposición de multiplicadores/ x^3-6*x+13*x+38*x+2

Factorizar el polinomio x^3-6*x+13*x+38*x+2

Expresión a simplificar:

Solución

Ha introducido [src] 
 3                        
x  - 6*x + 13*x + 38*x + 2
$$\left(38 x + \left(13 x + \left(x^{3} - 6 x\right)\right)\right) + 2$$ 
x^3 - 6*x + 13*x + 38*x + 2
Simplificación general [src] 
     3       
2 + x  + 45*x
$$x^{3} + 45 x + 2$$ 
2 + x^3 + 45*x
Factorización [src] 
/                                                 __________________ /          ___\\ /                                                 __________________ /          ___\\                                                      
|                                              3 /            _____  |  1   I*\/ 3 || |                                              3 /            _____  |  1   I*\/ 3 || /                                 __________________\
|                                              \/  27 + 108*\/ 211  *|- - - -------|| |                                              \/  27 + 108*\/ 211  *|- - + -------|| |                              3 /            _____ |
|                        45                                          \  2      2   /| |                        45                                          \  2      2   /| |                45            \/  27 + 108*\/ 211  |
|x + - ------------------------------------- + -------------------------------------|*|x + - ------------------------------------- + -------------------------------------|*|x + - --------------------- + ---------------------|
|         __________________ /          ___\                     3                  | |         __________________ /          ___\                     3                  | |         __________________             3          |
|      3 /            _____  |  1   I*\/ 3 |                                        | |      3 /            _____  |  1   I*\/ 3 |                                        | |      3 /            _____                         |
|      \/  27 + 108*\/ 211  *|- - - -------|                                        | |      \/  27 + 108*\/ 211  *|- - + -------|                                        | \      \/  27 + 108*\/ 211                          /
\                            \  2      2   /                                        / \                            \  2      2   /                                        /
$$\left(x + \left(\frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{27 + 108 \sqrt{211}}}{3} - \frac{45}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{27 + 108 \sqrt{211}}}\right)\right) \left(x + \left(- \frac{45}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{27 + 108 \sqrt{211}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{27 + 108 \sqrt{211}}}{3}\right)\right) \left(x + \left(- \frac{45}{\sqrt[3]{27 + 108 \sqrt{211}}} + \frac{\sqrt[3]{27 + 108 \sqrt{211}}}{3}\right)\right)$$ 
((x - 45/((27 + 108*sqrt(211))^(1/3)*(-1/2 - i*sqrt(3)/2)) + (27 + 108*sqrt(211))^(1/3)*(-1/2 - i*sqrt(3)/2)/3)*(x - 45/((27 + 108*sqrt(211))^(1/3)*(-1/2 + i*sqrt(3)/2)) + (27 + 108*sqrt(211))^(1/3)*(-1/2 + i*sqrt(3)/2)/3))*(x - 45/(27 + 108*sqrt(211))^(1/3) + (27 + 108*sqrt(211))^(1/3)/3)
Parte trigonométrica [src] 
     3       
2 + x  + 45*x
$$x^{3} + 45 x + 2$$ 
2 + x^3 + 45*x
Respuesta numérica [src] 
2.0 + x^3 + 45.0*x
2.0 + x^3 + 45.0*x
Compilar la expresión [src] 
     3       
2 + x  + 45*x
$$x^{3} + 45 x + 2$$ 
2 + x^3 + 45*x
Denominador común [src] 
     3       
2 + x  + 45*x
$$x^{3} + 45 x + 2$$ 
2 + x^3 + 45*x
Denominador racional [src] 
     3       
2 + x  + 45*x
$$x^{3} + 45 x + 2$$ 
2 + x^3 + 45*x
Potencias [src] 
     3       
2 + x  + 45*x
$$x^{3} + 45 x + 2$$ 
2 + x^3 + 45*x
Unión de expresiones racionales [src] 
      /      2\
2 + x*\45 + x /
$$x \left(x^{2} + 45\right) + 2$$ 
2 + x*(45 + x^2)
Combinatoria [src] 
     3       
2 + x  + 45*x
$$x^{3} + 45 x + 2$$ 
2 + x^3 + 45*x
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