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Simplificación de expresiones/ Descomposición de multiplicadores/ x^3+3*x^2-9*x+1

Factorizar el polinomio x^3+3*x^2-9*x+1

Expresión a simplificar:

Solución

Ha introducido [src] 
 3      2          
x  + 3*x  - 9*x + 1
$$\left(- 9 x + \left(x^{3} + 3 x^{2}\right)\right) + 1$$ 
x^3 + 3*x^2 - 9*x + 1
Simplificación general [src] 
     3            2
1 + x  - 9*x + 3*x
$$x^{3} + 3 x^{2} - 9 x + 1$$ 
1 + x^3 - 9*x + 3*x^2
Factorización [src] 
/                                                   __________________ /          ___\\ /                                                   __________________ /          ___\\                                                        
|                                                3 /              ___  |  1   I*\/ 3 || |                                                3 /              ___  |  1   I*\/ 3 || /                                   __________________\
|                                                \/  162 + 54*I*\/ 7  *|- - - -------|| |                                                \/  162 + 54*I*\/ 7  *|- - + -------|| |                                3 /              ___ |
|                          12                                          \  2      2   /| |                          12                                          \  2      2   /| |                  12            \/  162 + 54*I*\/ 7  |
|x + 1 + ------------------------------------- + -------------------------------------|*|x + 1 + ------------------------------------- + -------------------------------------|*|x + 1 + --------------------- + ---------------------|
|           __________________ /          ___\                     3                  | |           __________________ /          ___\                     3                  | |           __________________             3          |
|        3 /              ___  |  1   I*\/ 3 |                                        | |        3 /              ___  |  1   I*\/ 3 |                                        | |        3 /              ___                         |
|        \/  162 + 54*I*\/ 7  *|- - - -------|                                        | |        \/  162 + 54*I*\/ 7  *|- - + -------|                                        | \        \/  162 + 54*I*\/ 7                          /
\                              \  2      2   /                                        / \                              \  2      2   /                                        /
$$\left(x + \left(1 + \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{162 + 54 \sqrt{7} i}}{3} + \frac{12}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{162 + 54 \sqrt{7} i}}\right)\right) \left(x + \left(1 + \frac{12}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{162 + 54 \sqrt{7} i}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{162 + 54 \sqrt{7} i}}{3}\right)\right) \left(x + \left(1 + \frac{12}{\sqrt[3]{162 + 54 \sqrt{7} i}} + \frac{\sqrt[3]{162 + 54 \sqrt{7} i}}{3}\right)\right)$$ 
((x + 1 + 12/((162 + 54*i*sqrt(7))^(1/3)*(-1/2 - i*sqrt(3)/2)) + (162 + 54*i*sqrt(7))^(1/3)*(-1/2 - i*sqrt(3)/2)/3)*(x + 1 + 12/((162 + 54*i*sqrt(7))^(1/3)*(-1/2 + i*sqrt(3)/2)) + (162 + 54*i*sqrt(7))^(1/3)*(-1/2 + i*sqrt(3)/2)/3))*(x + 1 + 12/(162 + 54*i*sqrt(7))^(1/3) + (162 + 54*i*sqrt(7))^(1/3)/3)
Compilar la expresión [src] 
     3            2
1 + x  - 9*x + 3*x
$$x^{3} + 3 x^{2} - 9 x + 1$$ 
1 + x^3 - 9*x + 3*x^2
Unión de expresiones racionales [src] 
1 + x*(-9 + x*(3 + x))
$$x \left(x \left(x + 3\right) - 9\right) + 1$$ 
1 + x*(-9 + x*(3 + x))
Respuesta numérica [src] 
1.0 + x^3 + 3.0*x^2 - 9.0*x
1.0 + x^3 + 3.0*x^2 - 9.0*x
Denominador racional [src] 
     3            2
1 + x  - 9*x + 3*x
$$x^{3} + 3 x^{2} - 9 x + 1$$ 
1 + x^3 - 9*x + 3*x^2
Combinatoria [src] 
     3            2
1 + x  - 9*x + 3*x
$$x^{3} + 3 x^{2} - 9 x + 1$$ 
1 + x^3 - 9*x + 3*x^2
Parte trigonométrica [src] 
     3            2
1 + x  - 9*x + 3*x
$$x^{3} + 3 x^{2} - 9 x + 1$$ 
1 + x^3 - 9*x + 3*x^2
Potencias [src] 
     3            2
1 + x  - 9*x + 3*x
$$x^{3} + 3 x^{2} - 9 x + 1$$ 
1 + x^3 - 9*x + 3*x^2
Denominador común [src] 
     3            2
1 + x  - 9*x + 3*x
$$x^{3} + 3 x^{2} - 9 x + 1$$ 
1 + x^3 - 9*x + 3*x^2
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