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Factorizar el polinomio x^3-6*x^2+9*x+1

Expresión a simplificar:

Solución

Ha introducido [src]
 3      2          
x  - 6*x  + 9*x + 1
$$\left(9 x + \left(x^{3} - 6 x^{2}\right)\right) + 1$$
x^3 - 6*x^2 + 9*x + 1
Factorización [src]
/                                                     _______________                \ /                                                     _______________                \ /                                     _______________\
|                                                    /           ___  /          ___\| |                                                    /           ___  /          ___\| |                                    /           ___ |
|                                                   /  81   27*\/ 5   |  1   I*\/ 3 || |                                                   /  81   27*\/ 5   |  1   I*\/ 3 || |                                   /  81   27*\/ 5  |
|                                                3 /   -- + -------- *|- - - -------|| |                                                3 /   -- + -------- *|- - + -------|| |                                3 /   -- + -------- |
|                          3                     \/    2       2      \  2      2   /| |                          3                     \/    2       2      \  2      2   /| |                  3             \/    2       2     |
|x + -2 + ------------------------------------ + ------------------------------------|*|x + -2 + ------------------------------------ + ------------------------------------|*|x + -2 + -------------------- + --------------------|
|                              _______________                    3                  | |                              _______________                    3                  | |              _______________            3          |
|         /          ___\     /           ___                                        | |         /          ___\     /           ___                                        | |             /           ___                        |
|         |  1   I*\/ 3 |    /  81   27*\/ 5                                         | |         |  1   I*\/ 3 |    /  81   27*\/ 5                                         | |            /  81   27*\/ 5                         |
|         |- - - -------|*3 /   -- + --------                                        | |         |- - + -------|*3 /   -- + --------                                        | |         3 /   -- + --------                        |
\         \  2      2   / \/    2       2                                            / \         \  2      2   / \/    2       2                                            / \         \/    2       2                            /
$$\left(x + \left(-2 + \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}{3} + \frac{3}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}\right)\right) \left(x + \left(-2 + \frac{3}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}{3}\right)\right) \left(x + \left(-2 + \frac{3}{\sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}} + \frac{\sqrt[3]{\frac{27 \sqrt{5}}{2} + \frac{81}{2}}}{3}\right)\right)$$
((x - 2 + 3/((-1/2 - i*sqrt(3)/2)*(81/2 + 27*sqrt(5)/2)^(1/3)) + (81/2 + 27*sqrt(5)/2)^(1/3)*(-1/2 - i*sqrt(3)/2)/3)*(x - 2 + 3/((-1/2 + i*sqrt(3)/2)*(81/2 + 27*sqrt(5)/2)^(1/3)) + (81/2 + 27*sqrt(5)/2)^(1/3)*(-1/2 + i*sqrt(3)/2)/3))*(x - 2 + 3/(81/2 + 27*sqrt(5)/2)^(1/3) + (81/2 + 27*sqrt(5)/2)^(1/3)/3)
Simplificación general [src]
     3      2      
1 + x  - 6*x  + 9*x
$$x^{3} - 6 x^{2} + 9 x + 1$$
1 + x^3 - 6*x^2 + 9*x
Respuesta numérica [src]
1.0 + x^3 + 9.0*x - 6.0*x^2
1.0 + x^3 + 9.0*x - 6.0*x^2
Compilar la expresión [src]
     3      2      
1 + x  - 6*x  + 9*x
$$x^{3} - 6 x^{2} + 9 x + 1$$
1 + x^3 - 6*x^2 + 9*x
Denominador racional [src]
     3      2      
1 + x  - 6*x  + 9*x
$$x^{3} - 6 x^{2} + 9 x + 1$$
1 + x^3 - 6*x^2 + 9*x
Unión de expresiones racionales [src]
1 + x*(9 + x*(-6 + x))
$$x \left(x \left(x - 6\right) + 9\right) + 1$$
1 + x*(9 + x*(-6 + x))
Potencias [src]
     3      2      
1 + x  - 6*x  + 9*x
$$x^{3} - 6 x^{2} + 9 x + 1$$
1 + x^3 - 6*x^2 + 9*x
Denominador común [src]
     3      2      
1 + x  - 6*x  + 9*x
$$x^{3} - 6 x^{2} + 9 x + 1$$
1 + x^3 - 6*x^2 + 9*x
Parte trigonométrica [src]
     3      2      
1 + x  - 6*x  + 9*x
$$x^{3} - 6 x^{2} + 9 x + 1$$
1 + x^3 - 6*x^2 + 9*x
Combinatoria [src]
     3      2      
1 + x  - 6*x  + 9*x
$$x^{3} - 6 x^{2} + 9 x + 1$$
1 + x^3 - 6*x^2 + 9*x