Sr Examen
Factorizar el polinomio z^3-2*z^2+2*z-1
Solución
Ha introducido
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3 2 z - 2*z + 2*z - 1
$$\left(2 z + \left(z^{3} - 2 z^{2}\right)\right) - 1$$
z^3 - 2*z^2 + 2*z - 1
Simplificación general
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3 2 -1 + z - 2*z + 2*z
$$z^{3} - 2 z^{2} + 2 z - 1$$
-1 + z^3 - 2*z^2 + 2*z
Factorización
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/ ___\ / ___\
| 1 I*\/ 3 | | 1 I*\/ 3 |
(x - 1)*|x + - - + -------|*|x + - - - -------|
\ 2 2 / \ 2 2 /
$$\left(x - 1\right) \left(x + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)\right) \left(x + \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)\right)$$
((x - 1)*(x - 1/2 + i*sqrt(3)/2))*(x - 1/2 - i*sqrt(3)/2)
Parte trigonométrica
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3 2 -1 + z - 2*z + 2*z
$$z^{3} - 2 z^{2} + 2 z - 1$$
-1 + z^3 - 2*z^2 + 2*z
Compilar la expresión
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3 2 -1 + z - 2*z + 2*z
$$z^{3} - 2 z^{2} + 2 z - 1$$
-1 + z^3 - 2*z^2 + 2*z
Combinatoria
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/ 2 \ (-1 + z)*\1 + z - z/
$$\left(z - 1\right) \left(z^{2} - z + 1\right)$$
(-1 + z)*(1 + z^2 - z)
Unión de expresiones racionales
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-1 + z*(2 + z*(-2 + z))
$$z \left(z \left(z - 2\right) + 2\right) - 1$$
-1 + z*(2 + z*(-2 + z))
Denominador racional
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3 2 -1 + z - 2*z + 2*z
$$z^{3} - 2 z^{2} + 2 z - 1$$
-1 + z^3 - 2*z^2 + 2*z