Sr Examen
Factorizar el polinomio x+x^2/2+x^3/3+x^4/4
Solución
Ha introducido
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2 3 4
x x x
x + -- + -- + --
2 3 4
$$\frac{x^{4}}{4} + \left(\frac{x^{3}}{3} + \left(\frac{x^{2}}{2} + x\right)\right)$$
x + x^2/2 + x^3/3 + x^4/4
Descomposición de una fracción
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x + x^2/2 + x^3/3 + x^4/4
$$\frac{x^{4}}{4} + \frac{x^{3}}{3} + \frac{x^{2}}{2} + x$$
2 3 4
x x x
x + -- + -- + --
2 3 4
Factorización
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/ __________________ / ___\ \ / __________________ / ___\ \ / __________________ \ | / 1198 _____ | 1 I*\/ 3 | | | / 1198 _____ | 1 I*\/ 3 | | | / 1198 _____ | | 3 / ---- + 2*\/ 511 *|- - - -------| | | 3 / ---- + 2*\/ 511 *|- - + -------| | | 3 / ---- + 2*\/ 511 | | 4 \/ 27 \ 2 2 / 38 | | 4 \/ 27 \ 2 2 / 38 | | 4 \/ 27 38 | x*|x + - + -------------------------------------- - -----------------------------------------|*|x + - + -------------------------------------- - -----------------------------------------|*|x + - + ---------------------- - -------------------------| | 9 3 / ___\ __________________| | 9 3 / ___\ __________________| | 9 3 __________________| | | 1 I*\/ 3 | / 1198 _____ | | | 1 I*\/ 3 | / 1198 _____ | | / 1198 _____ | | 27*|- - - -------|*3 / ---- + 2*\/ 511 | | 27*|- - + -------|*3 / ---- + 2*\/ 511 | | 27*3 / ---- + 2*\/ 511 | \ \ 2 2 / \/ 27 / \ \ 2 2 / \/ 27 / \ \/ 27 /
$$x \left(x + \left(\frac{4}{9} + \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1198}{27} + 2 \sqrt{511}}}{3} - \frac{38}{27 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1198}{27} + 2 \sqrt{511}}}\right)\right) \left(x + \left(\frac{4}{9} - \frac{38}{27 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1198}{27} + 2 \sqrt{511}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1198}{27} + 2 \sqrt{511}}}{3}\right)\right) \left(x + \left(- \frac{38}{27 \sqrt[3]{\frac{1198}{27} + 2 \sqrt{511}}} + \frac{4}{9} + \frac{\sqrt[3]{\frac{1198}{27} + 2 \sqrt{511}}}{3}\right)\right)$$
((x*(x + 4/9 + (1198/27 + 2*sqrt(511))^(1/3)*(-1/2 - i*sqrt(3)/2)/3 - 38/(27*(-1/2 - i*sqrt(3)/2)*(1198/27 + 2*sqrt(511))^(1/3))))*(x + 4/9 + (1198/27 + 2*sqrt(511))^(1/3)*(-1/2 + i*sqrt(3)/2)/3 - 38/(27*(-1/2 + i*sqrt(3)/2)*(1198/27 + 2*sqrt(511))^(1/3))))*(x + 4/9 + (1198/27 + 2*sqrt(511))^(1/3)/3 - 38/(27*(1198/27 + 2*sqrt(511))^(1/3)))
Simplificación general
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/ 2 3\ | x x x | x*|1 + - + -- + --| \ 2 3 4 /
$$x \left(\frac{x^{3}}{4} + \frac{x^{2}}{3} + \frac{x}{2} + 1\right)$$
x*(1 + x/2 + x^2/3 + x^3/4)
Denominador común
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2 3 4
x x x
x + -- + -- + --
2 3 4
$$\frac{x^{4}}{4} + \frac{x^{3}}{3} + \frac{x^{2}}{2} + x$$
x + x^2/2 + x^3/3 + x^4/4
Potencias
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2 3 4
x x x
x + -- + -- + --
2 3 4
$$\frac{x^{4}}{4} + \frac{x^{3}}{3} + \frac{x^{2}}{2} + x$$
x + x^2/2 + x^3/3 + x^4/4
Compilar la expresión
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2 3 4
x x x
x + -- + -- + --
2 3 4
$$\frac{x^{4}}{4} + \frac{x^{3}}{3} + \frac{x^{2}}{2} + x$$
x + x^2/2 + x^3/3 + x^4/4
Combinatoria
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/ 3 2 \
x*\12 + 3*x + 4*x + 6*x/
--------------------------
12
$$\frac{x \left(3 x^{3} + 4 x^{2} + 6 x + 12\right)}{12}$$
x*(12 + 3*x^3 + 4*x^2 + 6*x)/12
Parte trigonométrica
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2 3 4
x x x
x + -- + -- + --
2 3 4
$$\frac{x^{4}}{4} + \frac{x^{3}}{3} + \frac{x^{2}}{2} + x$$
x + x^2/2 + x^3/3 + x^4/4
Respuesta numérica
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x + 0.25*x^4 + 0.5*x^2 + 0.333333333333333*x^3
x + 0.25*x^4 + 0.5*x^2 + 0.333333333333333*x^3
Denominador racional
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4 3 2
6*x + 8*x + 12*x + 24*x
--------------------------
24
$$\frac{6 x^{4} + 8 x^{3} + 12 x^{2} + 24 x}{24}$$
(6*x^4 + 8*x^3 + 12*x^2 + 24*x)/24
Unión de expresiones racionales
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/ 3 2 \
x*\12 + 3*x + 4*x + 6*x/
--------------------------
12
$$\frac{x \left(3 x^{3} + 4 x^{2} + 6 x + 12\right)}{12}$$
x*(12 + 3*x^3 + 4*x^2 + 6*x)/12