Sr Examen
Factorizar el polinomio z^3-19*z^2/10-z/5+1/10
Solución
Ha introducido
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2
3 19*z z 1
z - ----- - - + --
10 5 10
$$\left(- \frac{z}{5} + \left(z^{3} - \frac{19 z^{2}}{10}\right)\right) + \frac{1}{10}$$
z^3 - 19*z^2/10 - z/5 + 1/10
Simplificación general
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2 1 3 19*z z -- + z - ----- - - 10 10 5
$$z^{3} - \frac{19 z^{2}}{10} - \frac{z}{5} + \frac{1}{10}$$
1/10 + z^3 - 19*z^2/10 - z/5
Factorización
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/ _____________________ \ / _____________________ \ / _____________________ \ | / _______ / ___\ | | / _______ / ___\ | | / _______ | | 19 / 7219 I*\/ 25005 | 1 I*\/ 3 | 421 | | 19 / 7219 I*\/ 25005 | 1 I*\/ 3 | 421 | | 19 / 7219 I*\/ 25005 421 | |x + - -- - 3 / ----- + ----------- *|- - - -------| - ----------------------------------------------|*|x + - -- - 3 / ----- + ----------- *|- - + -------| - ----------------------------------------------|*|x + - -- - 3 / ----- + ----------- - ------------------------------| | 30 \/ 27000 900 \ 2 2 / _____________________| | 30 \/ 27000 900 \ 2 2 / _____________________| | 30 \/ 27000 900 _____________________| | / ___\ / _______ | | / ___\ / _______ | | / _______ | | | 1 I*\/ 3 | / 7219 I*\/ 25005 | | | 1 I*\/ 3 | / 7219 I*\/ 25005 | | / 7219 I*\/ 25005 | | 900*|- - - -------|*3 / ----- + ----------- | | 900*|- - + -------|*3 / ----- + ----------- | | 900*3 / ----- + ----------- | \ \ 2 2 / \/ 27000 900 / \ \ 2 2 / \/ 27000 900 / \ \/ 27000 900 /
$$\left(x + \left(- \frac{19}{30} - \frac{421}{900 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{7219}{27000} + \frac{\sqrt{25005} i}{900}}} - \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{7219}{27000} + \frac{\sqrt{25005} i}{900}}\right)\right) \left(x + \left(- \frac{19}{30} - \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{7219}{27000} + \frac{\sqrt{25005} i}{900}} - \frac{421}{900 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{7219}{27000} + \frac{\sqrt{25005} i}{900}}}\right)\right) \left(x + \left(- \frac{19}{30} - \sqrt[3]{\frac{7219}{27000} + \frac{\sqrt{25005} i}{900}} - \frac{421}{900 \sqrt[3]{\frac{7219}{27000} + \frac{\sqrt{25005} i}{900}}}\right)\right)$$
((x - 19/30 - (7219/27000 + i*sqrt(25005)/900)^(1/3)*(-1/2 - i*sqrt(3)/2) - 421/(900*(-1/2 - i*sqrt(3)/2)*(7219/27000 + i*sqrt(25005)/900)^(1/3)))*(x - 19/30 - (7219/27000 + i*sqrt(25005)/900)^(1/3)*(-1/2 + i*sqrt(3)/2) - 421/(900*(-1/2 + i*sqrt(3)/2)*(7219/27000 + i*sqrt(25005)/900)^(1/3))))*(x - 19/30 - (7219/27000 + i*sqrt(25005)/900)^(1/3) - 421/(900*(7219/27000 + i*sqrt(25005)/900)^(1/3)))
Descomposición de una fracción
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1/10 + z^3 - 19*z^2/10 - z/5
$$z^{3} - \frac{19 z^{2}}{10} - \frac{z}{5} + \frac{1}{10}$$
2 1 3 19*z z -- + z - ----- - - 10 10 5
Parte trigonométrica
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2 1 3 19*z z -- + z - ----- - - 10 10 5
$$z^{3} - \frac{19 z^{2}}{10} - \frac{z}{5} + \frac{1}{10}$$
1/10 + z^3 - 19*z^2/10 - z/5
Combinatoria
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2 1 3 19*z z -- + z - ----- - - 10 10 5
$$z^{3} - \frac{19 z^{2}}{10} - \frac{z}{5} + \frac{1}{10}$$
1/10 + z^3 - 19*z^2/10 - z/5
Denominador racional
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2 3
50 - 950*z - 100*z + 500*z
----------------------------
500
$$\frac{500 z^{3} - 950 z^{2} - 100 z + 50}{500}$$
(50 - 950*z^2 - 100*z + 500*z^3)/500
Unión de expresiones racionales
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1 + z*(-2 + z*(-19 + 10*z))
---------------------------
10
$$\frac{z \left(z \left(10 z - 19\right) - 2\right) + 1}{10}$$
(1 + z*(-2 + z*(-19 + 10*z)))/10
Compilar la expresión
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2 1 3 19*z z -- + z - ----- - - 10 10 5
$$z^{3} - \frac{19 z^{2}}{10} - \frac{z}{5} + \frac{1}{10}$$
1/10 + z^3 - 19*z^2/10 - z/5
Potencias
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2 1 3 19*z z -- + z - ----- - - 10 10 5
$$z^{3} - \frac{19 z^{2}}{10} - \frac{z}{5} + \frac{1}{10}$$
1/10 + z^3 - 19*z^2/10 - z/5
Denominador común
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2 1 3 19*z z -- + z - ----- - - 10 10 5
$$z^{3} - \frac{19 z^{2}}{10} - \frac{z}{5} + \frac{1}{10}$$
1/10 + z^3 - 19*z^2/10 - z/5