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Simplificación de expresiones/ Descomposición de multiplicadores/ x+x^2/2+x^3/3+x^4/4

Factorizar el polinomio x+x^2/2+x^3/3+x^4/4

Expresión a simplificar:

Solución

Ha introducido [src] 
     2    3    4
    x    x    x 
x + -- + -- + --
    2    3    4
x44+(x33+(x22+x))\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 [src] 
x + x^2/2 + x^3/3 + x^4/4
x44+x33+x22+x\frac{x^{4}}{4} + \frac{x^{3}}{3} + \frac{x^{2}}{2} + x 
     2    3    4
    x    x    x 
x + -- + -- + --
    2    3    4
Factorización [src] 
  /            __________________ /          ___\                                            \ /            __________________ /          ___\                                            \ /            __________________                            \
  |           / 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(x+(49+(−12−3i2)119827+251133−3827(−12−3i2)119827+25113))(x+(49−3827(−12+3i2)119827+25113+(−12+3i2)119827+251133))(x+(−3827119827+25113+49+119827+251133))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 [src] 
  /         2    3\
  |    x   x    x |
x*|1 + - + -- + --|
  \    2   3    4 /
x(x34+x23+x2+1)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 [src] 
     2    3    4
    x    x    x 
x + -- + -- + --
    2    3    4
x44+x33+x22+x\frac{x^{4}}{4} + \frac{x^{3}}{3} + \frac{x^{2}}{2} + x 
x + x^2/2 + x^3/3 + x^4/4
Potencias [src] 
     2    3    4
    x    x    x 
x + -- + -- + --
    2    3    4
x44+x33+x22+x\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 [src] 
     2    3    4
    x    x    x 
x + -- + -- + --
    2    3    4
x44+x33+x22+x\frac{x^{4}}{4} + \frac{x^{3}}{3} + \frac{x^{2}}{2} + x 
x + x^2/2 + x^3/3 + x^4/4
Combinatoria [src] 
  /        3      2      \
x*\12 + 3*x  + 4*x  + 6*x/
--------------------------
            12
x(3x3+4x2+6x+12)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 [src] 
     2    3    4
    x    x    x 
x + -- + -- + --
    2    3    4
x44+x33+x22+x\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 [src] 
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 [src] 
   4      3       2       
6*x  + 8*x  + 12*x  + 24*x
--------------------------
            24
6x4+8x3+12x2+24x24\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 [src] 
  /        3      2      \
x*\12 + 3*x  + 4*x  + 6*x/
--------------------------
            12
x(3x3+4x2+6x+12)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
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