Sr Examen
Factorizar el polinomio x^4+x^3/2-4*x^2-3*x-1/2
Solución
Ha introducido
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3
4 x 2 1
x + -- - 4*x - 3*x - -
2 2
$$\left(- 3 x + \left(- 4 x^{2} + \left(x^{4} + \frac{x^{3}}{2}\right)\right)\right) - \frac{1}{2}$$
x^4 + x^3/2 - 4*x^2 - 3*x - 1/2
Factorización
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/ _______________ \ / _______________ \ / _______________ \
| / _____ / ___\ | | / _____ / ___\ | | / _____ |
| / 1 I*\/ 687 | 1 I*\/ 3 | 4 | | / 1 I*\/ 687 | 1 I*\/ 3 | 4 | | / 1 I*\/ 687 4 |
(x + 1/2)*|x + - 3 / - + --------- *|- - - -------| - --------------------------------------|*|x + - 3 / - + --------- *|- - + -------| - --------------------------------------|*|x + - 3 / - + --------- - ----------------------|
| \/ 2 18 \ 2 2 / _______________ | | \/ 2 18 \ 2 2 / _______________ | | \/ 2 18 _______________|
| / _____ / ___\| | / _____ / ___\| | / _____ |
| / 1 I*\/ 687 | 1 I*\/ 3 || | / 1 I*\/ 687 | 1 I*\/ 3 || | / 1 I*\/ 687 |
| 3*3 / - + --------- *|- - - -------|| | 3*3 / - + --------- *|- - + -------|| | 3*3 / - + --------- |
\ \/ 2 18 \ 2 2 // \ \/ 2 18 \ 2 2 // \ \/ 2 18 /
$$\left(x + \frac{1}{2}\right) \left(x + \left(- \frac{4}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}} - \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}\right)\right) \left(x + \left(- \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}} - \frac{4}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}}\right)\right) \left(x + \left(- \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}} - \frac{4}{3 \sqrt[3]{\frac{1}{2} + \frac{\sqrt{687} i}{18}}}\right)\right)$$
(((x + 1/2)*(x - (1/2 + i*sqrt(687)/18)^(1/3)*(-1/2 - i*sqrt(3)/2) - 4/(3*(1/2 + i*sqrt(687)/18)^(1/3)*(-1/2 - i*sqrt(3)/2))))*(x - (1/2 + i*sqrt(687)/18)^(1/3)*(-1/2 + i*sqrt(3)/2) - 4/(3*(1/2 + i*sqrt(687)/18)^(1/3)*(-1/2 + i*sqrt(3)/2))))*(x - (1/2 + i*sqrt(687)/18)^(1/3) - 4/(3*(1/2 + i*sqrt(687)/18)^(1/3)))
Descomposición de una fracción
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-1/2 + x^4 + x^3/2 - 4*x^2 - 3*x
$$x^{4} + \frac{x^{3}}{2} - 4 x^{2} - 3 x - \frac{1}{2}$$
3 1 4 x 2 - - + x + -- - 4*x - 3*x 2 2
Simplificación general
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3 1 4 x 2 - - + x + -- - 4*x - 3*x 2 2
$$x^{4} + \frac{x^{3}}{2} - 4 x^{2} - 3 x - \frac{1}{2}$$
-1/2 + x^4 + x^3/2 - 4*x^2 - 3*x
Unión de expresiones racionales
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-1 + x*(-6 + x*(-8 + x*(1 + 2*x)))
----------------------------------
2
$$\frac{x \left(x \left(x \left(2 x + 1\right) - 8\right) - 6\right) - 1}{2}$$
(-1 + x*(-6 + x*(-8 + x*(1 + 2*x))))/2
Parte trigonométrica
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3 1 4 x 2 - - + x + -- - 4*x - 3*x 2 2
$$x^{4} + \frac{x^{3}}{2} - 4 x^{2} - 3 x - \frac{1}{2}$$
-1/2 + x^4 + x^3/2 - 4*x^2 - 3*x
Denominador común
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3 1 4 x 2 - - + x + -- - 4*x - 3*x 2 2
$$x^{4} + \frac{x^{3}}{2} - 4 x^{2} - 3 x - \frac{1}{2}$$
-1/2 + x^4 + x^3/2 - 4*x^2 - 3*x
Denominador racional
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2 3 4
-2 - 16*x - 12*x + 2*x + 4*x
-------------------------------
4
$$\frac{4 x^{4} + 2 x^{3} - 16 x^{2} - 12 x - 2}{4}$$
(-2 - 16*x^2 - 12*x + 2*x^3 + 4*x^4)/4
Compilar la expresión
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3 1 4 x 2 - - + x + -- - 4*x - 3*x 2 2
$$x^{4} + \frac{x^{3}}{2} - 4 x^{2} - 3 x - \frac{1}{2}$$
-1/2 + x^4 + x^3/2 - 4*x^2 - 3*x
Combinatoria
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/ 3 \
(1 + 2*x)*\-1 + x - 4*x/
-------------------------
2
$$\frac{\left(2 x + 1\right) \left(x^{3} - 4 x - 1\right)}{2}$$
(1 + 2*x)*(-1 + x^3 - 4*x)/2
Potencias
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3 1 4 x 2 - - + x + -- - 4*x - 3*x 2 2
$$x^{4} + \frac{x^{3}}{2} - 4 x^{2} - 3 x - \frac{1}{2}$$
-1/2 + x^4 + x^3/2 - 4*x^2 - 3*x
Respuesta numérica
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-0.5 + x^4 + 0.5*x^3 - 4.0*x^2 - 3.0*x
-0.5 + x^4 + 0.5*x^3 - 4.0*x^2 - 3.0*x