Sr Examen
Factorizar el polinomio x^3+x^4/2-6*x-2*x^2
Solución
Ha introducido
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4
3 x 2
x + -- - 6*x - 2*x
2
$$- 2 x^{2} + \left(- 6 x + \left(\frac{x^{4}}{2} + x^{3}\right)\right)$$
x^3 + x^4/2 - 6*x - 2*x^2
Descomposición de una fracción
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x^3 + x^4/2 - 6*x - 2*x^2
$$\frac{x^{4}}{2} + x^{3} - 2 x^{2} - 6 x$$
4
3 x 2
x + -- - 6*x - 2*x
2
Simplificación general
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/ 3 2\
x*\-12 + x - 4*x + 2*x /
-------------------------
2
$$\frac{x \left(x^{3} + 2 x^{2} - 4 x - 12\right)}{2}$$
x*(-12 + x^3 - 4*x + 2*x^2)/2
Factorización
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/ _________________ \ / _________________ \ / _________________ \ | / _____ / ___\ | | / _____ / ___\ | | / _____ | | 2 / 118 2*\/ 273 | 1 I*\/ 3 | 16 | | 2 / 118 2*\/ 273 | 1 I*\/ 3 | 16 | | 2 / 118 2*\/ 273 16 | x*|x + - - 3 / --- + --------- *|- - - -------| - ----------------------------------------|*|x + - - 3 / --- + --------- *|- - + -------| - ----------------------------------------|*|x + - - 3 / --- + --------- - ------------------------| | 3 \/ 27 9 \ 2 2 / _________________| | 3 \/ 27 9 \ 2 2 / _________________| | 3 \/ 27 9 _________________| | / ___\ / _____ | | / ___\ / _____ | | / _____ | | | 1 I*\/ 3 | / 118 2*\/ 273 | | | 1 I*\/ 3 | / 118 2*\/ 273 | | / 118 2*\/ 273 | | 9*|- - - -------|*3 / --- + --------- | | 9*|- - + -------|*3 / --- + --------- | | 9*3 / --- + --------- | \ \ 2 2 / \/ 27 9 / \ \ 2 2 / \/ 27 9 / \ \/ 27 9 /
$$x \left(x + \left(\frac{2}{3} - \frac{16}{9 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{2 \sqrt{273}}{9} + \frac{118}{27}}} - \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{2 \sqrt{273}}{9} + \frac{118}{27}}\right)\right) \left(x + \left(\frac{2}{3} - \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{2 \sqrt{273}}{9} + \frac{118}{27}} - \frac{16}{9 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{2 \sqrt{273}}{9} + \frac{118}{27}}}\right)\right) \left(x + \left(- \sqrt[3]{\frac{2 \sqrt{273}}{9} + \frac{118}{27}} - \frac{16}{9 \sqrt[3]{\frac{2 \sqrt{273}}{9} + \frac{118}{27}}} + \frac{2}{3}\right)\right)$$
((x*(x + 2/3 - (118/27 + 2*sqrt(273)/9)^(1/3)*(-1/2 - i*sqrt(3)/2) - 16/(9*(-1/2 - i*sqrt(3)/2)*(118/27 + 2*sqrt(273)/9)^(1/3))))*(x + 2/3 - (118/27 + 2*sqrt(273)/9)^(1/3)*(-1/2 + i*sqrt(3)/2) - 16/(9*(-1/2 + i*sqrt(3)/2)*(118/27 + 2*sqrt(273)/9)^(1/3))))*(x + 2/3 - (118/27 + 2*sqrt(273)/9)^(1/3) - 16/(9*(118/27 + 2*sqrt(273)/9)^(1/3)))
Parte trigonométrica
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4
3 x 2
x + -- - 6*x - 2*x
2
$$\frac{x^{4}}{2} + x^{3} - 2 x^{2} - 6 x$$
x^3 + x^4/2 - 6*x - 2*x^2
Unión de expresiones racionales
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/ 2 \
x*\-12 - 4*x + x *(2 + x)/
--------------------------
2
$$\frac{x \left(x^{2} \left(x + 2\right) - 4 x - 12\right)}{2}$$
x*(-12 - 4*x + x^2*(2 + x))/2
Combinatoria
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/ 3 2\
x*\-12 + x - 4*x + 2*x /
-------------------------
2
$$\frac{x \left(x^{3} + 2 x^{2} - 4 x - 12\right)}{2}$$
x*(-12 + x^3 - 4*x + 2*x^2)/2
Denominador común
[src]
4
3 x 2
x + -- - 6*x - 2*x
2
$$\frac{x^{4}}{2} + x^{3} - 2 x^{2} - 6 x$$
x^3 + x^4/2 - 6*x - 2*x^2
Compilar la expresión
[src]
4
3 x 2
x + -- - 6*x - 2*x
2
$$\frac{x^{4}}{2} + x^{3} - 2 x^{2} - 6 x$$
x^3 + x^4/2 - 6*x - 2*x^2
Denominador racional
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4 2 3
x - 12*x - 4*x + 2*x
-----------------------
2
$$\frac{x^{4} + 2 x^{3} - 4 x^{2} - 12 x}{2}$$
(x^4 - 12*x - 4*x^2 + 2*x^3)/2
Potencias
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4
3 x 2
x + -- - 6*x - 2*x
2
$$\frac{x^{4}}{2} + x^{3} - 2 x^{2} - 6 x$$
x^3 + x^4/2 - 6*x - 2*x^2