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Simplificación de expresiones/ Descomposición de multiplicadores/ x-2*x^3/3+x^5/5

Factorizar el polinomio x-2*x^3/3+x^5/5

Expresión a simplificar:

Solución

Ha introducido [src] 
       3    5
    2*x    x 
x - ---- + --
     3     5
x55+(x−2x33)\frac{x^{5}}{5} + \left(x - \frac{2 x^{3}}{3}\right) 
x - 2*x^3/3 + x^5/5
Simplificación general [src] 
       3    5
    2*x    x 
x - ---- + --
     3     5
x55−2x33+x\frac{x^{5}}{5} - \frac{2 x^{3}}{3} + x 
x - 2*x^3/3 + x^5/5
Factorización [src] 
  /             /    /    ___\\              /    /    ___\\\ /             /    /    ___\\              /    /    ___\\\ /               /    /    ___\\              /    /    ___\\\ /               /    /    ___\\              /    /    ___\\\
  |             |    |2*\/ 5 ||              |    |2*\/ 5 ||| |             |    |2*\/ 5 ||              |    |2*\/ 5 ||| |               |    |2*\/ 5 ||              |    |2*\/ 5 ||| |               |    |2*\/ 5 ||              |    |2*\/ 5 |||
  |             |atan|-------||              |atan|-------||| |             |atan|-------||              |atan|-------||| |               |atan|-------||              |atan|-------||| |               |atan|-------||              |atan|-------|||
  |    4 ___    |    \   5   /|     4 ___    |    \   5   /|| |    4 ___    |    \   5   /|     4 ___    |    \   5   /|| |      4 ___    |    \   5   /|     4 ___    |    \   5   /|| |      4 ___    |    \   5   /|     4 ___    |    \   5   /||
x*|x + \/ 5 *cos|-------------| + I*\/ 5 *sin|-------------||*|x + \/ 5 *cos|-------------| - I*\/ 5 *sin|-------------||*|x + - \/ 5 *cos|-------------| + I*\/ 5 *sin|-------------||*|x + - \/ 5 *cos|-------------| - I*\/ 5 *sin|-------------||
  \             \      2      /              \      2      // \             \      2      /              \      2      // \               \      2      /              \      2      // \               \      2      /              \      2      //
x(x+(54cos⁡(atan⁡(255)2)+54isin⁡(atan⁡(255)2)))(x+(54cos⁡(atan⁡(255)2)−54isin⁡(atan⁡(255)2)))(x+(−54cos⁡(atan⁡(255)2)+54isin⁡(atan⁡(255)2)))(x+(−54cos⁡(atan⁡(255)2)−54isin⁡(atan⁡(255)2)))x \left(x + \left(\sqrt[4]{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)}}{2} \right)} + \sqrt[4]{5} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)}}{2} \right)}\right)\right) \left(x + \left(\sqrt[4]{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)}}{2} \right)} - \sqrt[4]{5} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)}}{2} \right)}\right)\right) \left(x + \left(- \sqrt[4]{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)}}{2} \right)} + \sqrt[4]{5} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)}}{2} \right)}\right)\right) \left(x + \left(- \sqrt[4]{5} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)}}{2} \right)} - \sqrt[4]{5} i \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)}}{2} \right)}\right)\right) 
(((x*(x + 5^(1/4)*cos(atan(2*sqrt(5)/5)/2) + i*5^(1/4)*sin(atan(2*sqrt(5)/5)/2)))*(x + 5^(1/4)*cos(atan(2*sqrt(5)/5)/2) - i*5^(1/4)*sin(atan(2*sqrt(5)/5)/2)))*(x - 5^(1/4)*cos(atan(2*sqrt(5)/5)/2) + i*5^(1/4)*sin(atan(2*sqrt(5)/5)/2)))*(x - 5^(1/4)*cos(atan(2*sqrt(5)/5)/2) - i*5^(1/4)*sin(atan(2*sqrt(5)/5)/2))
Descomposición de una fracción [src] 
x - 2*x^3/3 + x^5/5
x55−2x33+x\frac{x^{5}}{5} - \frac{2 x^{3}}{3} + x 
       3    5
    2*x    x 
x - ---- + --
     3     5
Respuesta numérica [src] 
x + 0.2*x^5 - 0.666666666666667*x^3
x + 0.2*x^5 - 0.666666666666667*x^3
Combinatoria [src] 
  /         2      4\
x*\15 - 10*x  + 3*x /
---------------------
          15
x(3x4−10x2+15)15\frac{x \left(3 x^{4} - 10 x^{2} + 15\right)}{15} 
x*(15 - 10*x^2 + 3*x^4)/15
Compilar la expresión [src] 
       3    5
    2*x    x 
x - ---- + --
     3     5
x55−2x33+x\frac{x^{5}}{5} - \frac{2 x^{3}}{3} + x 
x - 2*x^3/3 + x^5/5
Denominador racional [src] 
      3      5       
- 10*x  + 3*x  + 15*x
---------------------
          15
3x5−10x3+15x15\frac{3 x^{5} - 10 x^{3} + 15 x}{15} 
(-10*x^3 + 3*x^5 + 15*x)/15
Unión de expresiones racionales [src] 
  /         2      4\
x*\15 - 10*x  + 3*x /
---------------------
          15
x(3x4−10x2+15)15\frac{x \left(3 x^{4} - 10 x^{2} + 15\right)}{15} 
x*(15 - 10*x^2 + 3*x^4)/15
Denominador común [src] 
       3    5
    2*x    x 
x - ---- + --
     3     5
x55−2x33+x\frac{x^{5}}{5} - \frac{2 x^{3}}{3} + x 
x - 2*x^3/3 + x^5/5
Parte trigonométrica [src] 
       3    5
    2*x    x 
x - ---- + --
     3     5
x55−2x33+x\frac{x^{5}}{5} - \frac{2 x^{3}}{3} + x 
x - 2*x^3/3 + x^5/5
Potencias [src] 
       3    5
    2*x    x 
x - ---- + --
     3     5
x55−2x33+x\frac{x^{5}}{5} - \frac{2 x^{3}}{3} + x 
x - 2*x^3/3 + x^5/5
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