Sr Examen
Factorizar el polinomio z^3+z^2/2+z/2+10
Solución
Ha introducido
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2
3 z z
z + -- + - + 10
2 2
$$\left(\frac{z}{2} + \left(z^{3} + \frac{z^{2}}{2}\right)\right) + 10$$
z^3 + z^2/2 + z/2 + 10
Descomposición de una fracción
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10 + z^3 + z/2 + z^2/2
$$z^{3} + \frac{z^{2}}{2} + \frac{z}{2} + 10$$
2
3 z z
10 + z + - + --
2 2
Factorización
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/ ___________________ \ / ___________________ \ / ___________________ \ | / _______ / ___\ | | / _______ / ___\ | | / _______ | | / 9*\/ 14189 | 1 I*\/ 3 | | | / 9*\/ 14189 | 1 I*\/ 3 | | | / 9*\/ 14189 | | 3 / 134 + ----------- *|- - - -------| | | 3 / 134 + ----------- *|- - + -------| | | 3 / 134 + ----------- | | 1 \/ 8 \ 2 2 / 5 | | 1 \/ 8 \ 2 2 / 5 | | 1 \/ 8 5 | |x + - + ---------------------------------------- - -------------------------------------------|*|x + - + ---------------------------------------- - -------------------------------------------|*|x + - + ------------------------ - ---------------------------| | 6 3 ___________________ | | 6 3 ___________________ | | 6 3 ___________________| | / _______ / ___\| | / _______ / ___\| | / _______ | | / 9*\/ 14189 | 1 I*\/ 3 || | / 9*\/ 14189 | 1 I*\/ 3 || | / 9*\/ 14189 | | 12*3 / 134 + ----------- *|- - - -------|| | 12*3 / 134 + ----------- *|- - + -------|| | 12*3 / 134 + ----------- | \ \/ 8 \ 2 2 // \ \/ 8 \ 2 2 // \ \/ 8 /
$$\left(x + \left(\frac{1}{6} + \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{134 + \frac{9 \sqrt{14189}}{8}}}{3} - \frac{5}{12 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{134 + \frac{9 \sqrt{14189}}{8}}}\right)\right) \left(x + \left(\frac{1}{6} - \frac{5}{12 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{134 + \frac{9 \sqrt{14189}}{8}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{134 + \frac{9 \sqrt{14189}}{8}}}{3}\right)\right) \left(x + \left(- \frac{5}{12 \sqrt[3]{134 + \frac{9 \sqrt{14189}}{8}}} + \frac{1}{6} + \frac{\sqrt[3]{134 + \frac{9 \sqrt{14189}}{8}}}{3}\right)\right)$$
((x + 1/6 + (134 + 9*sqrt(14189)/8)^(1/3)*(-1/2 - i*sqrt(3)/2)/3 - 5/(12*(134 + 9*sqrt(14189)/8)^(1/3)*(-1/2 - i*sqrt(3)/2)))*(x + 1/6 + (134 + 9*sqrt(14189)/8)^(1/3)*(-1/2 + i*sqrt(3)/2)/3 - 5/(12*(134 + 9*sqrt(14189)/8)^(1/3)*(-1/2 + i*sqrt(3)/2))))*(x + 1/6 + (134 + 9*sqrt(14189)/8)^(1/3)/3 - 5/(12*(134 + 9*sqrt(14189)/8)^(1/3)))
Simplificación general
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2
3 z z
10 + z + - + --
2 2
$$z^{3} + \frac{z^{2}}{2} + \frac{z}{2} + 10$$
10 + z^3 + z/2 + z^2/2
Compilar la expresión
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2
3 z z
10 + z + - + --
2 2
$$z^{3} + \frac{z^{2}}{2} + \frac{z}{2} + 10$$
10 + z^3 + z/2 + z^2/2
Denominador común
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2
3 z z
10 + z + - + --
2 2
$$z^{3} + \frac{z^{2}}{2} + \frac{z}{2} + 10$$
10 + z^3 + z/2 + z^2/2
Combinatoria
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2
3 z z
10 + z + - + --
2 2
$$z^{3} + \frac{z^{2}}{2} + \frac{z}{2} + 10$$
10 + z^3 + z/2 + z^2/2
Unión de expresiones racionales
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20 + z*(1 + z*(1 + 2*z))
------------------------
2
$$\frac{z \left(z \left(2 z + 1\right) + 1\right) + 20}{2}$$
(20 + z*(1 + z*(1 + 2*z)))/2
Denominador racional
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2 3
20 + z + z + 2*z
------------------
2
$$\frac{2 z^{3} + z^{2} + z + 20}{2}$$
(20 + z + z^2 + 2*z^3)/2
Potencias
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2
3 z z
10 + z + - + --
2 2
$$z^{3} + \frac{z^{2}}{2} + \frac{z}{2} + 10$$
10 + z^3 + z/2 + z^2/2
Parte trigonométrica
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2
3 z z
10 + z + - + --
2 2
$$z^{3} + \frac{z^{2}}{2} + \frac{z}{2} + 10$$
10 + z^3 + z/2 + z^2/2