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Simplificación de expresiones/ Descomposición de multiplicadores/ x^2+x^3/3+x^6/3

Factorizar el polinomio x^2+x^3/3+x^6/3

Expresión a simplificar:

Solución

Ha introducido [src] 
      3    6
 2   x    x 
x  + -- + --
     3    3
x63+(x33+x2)\frac{x^{6}}{3} + \left(\frac{x^{3}}{3} + x^{2}\right) 
x^2 + x^3/3 + x^6/3
Descomposición de una fracción [src] 
x^2 + x^3/3 + x^6/3
x63+x33+x2\frac{x^{6}}{3} + \frac{x^{3}}{3} + x^{2} 
      3    6
 2   x    x 
x  + -- + --
     3    3
Simplificación general [src] 
 2 /         4\
x *\3 + x + x /
---------------
       3
x2(x4+x+3)3\frac{x^{2} \left(x^{4} + x + 3\right)}{3} 
x^2*(3 + x + x^4)/3
Factorización [src] 
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  |                                                                                /                                  ________________                                                               | |                                                                                  /                                  ________________                                                               | |                                                                                  /                                  ________________                                                               | |                    /                                  ________________                                                                                                                             |
  |                                                                               /                                  /          _____                                                                | |                                                                                 /                                  /          _____                                                                | |                                                                                 /                                  /          _____                                                                | |                   /                                  /          _____                                                                                                                              |
  |                                                                              /               2                  /  1    I*\/ 255                                  2                              | |                                                                                /               2                  /  1    I*\/ 255                                  2                              | |                                                                                /               2                  /  1    I*\/ 255                                  2                              | |                  /               2                  /  1    I*\/ 255                                  2                                                                                            |
  |                                                                             /    - --------------------- - 2*3 /   -- + ---------  + ----------------------------------------------------------- | |                                                                               /    - --------------------- - 2*3 /   -- + ---------  - ----------------------------------------------------------- | |                                                                               /    - --------------------- - 2*3 /   -- + ---------  - ----------------------------------------------------------- | |                 /    - --------------------- - 2*3 /   -- + ---------  + -----------------------------------------------------------                                                               |
  |              _________________________________________________             /            ________________     \/    16       16                 _________________________________________________ | |                _________________________________________________             /            ________________     \/    16       16                 _________________________________________________ | |                _________________________________________________             /            ________________     \/    16       16                 _________________________________________________ | |                /            ________________     \/    16       16                 _________________________________________________              _________________________________________________|
  |             /                                ________________             /            /          _____                                       /                                ________________  | |               /                                ________________             /            /          _____                                       /                                ________________  | |               /                                ________________             /            /          _____                                       /                                ________________  | |               /            /          _____                                       /                                ________________              /                                ________________ |
  |            /                                /          _____             /            /  1    I*\/ 255                                       /                                /          _____   | |              /                                /          _____             /            /  1    I*\/ 255                                       /                                /          _____   | |              /                                /          _____             /            /  1    I*\/ 255                                       /                                /          _____   | |              /            /  1    I*\/ 255                                       /                                /          _____              /                                /          _____  |
  |           /             2                  /  1    I*\/ 255             /          3 /   -- + ---------                                     /             2                  /  1    I*\/ 255    | |             /             2                  /  1    I*\/ 255             /          3 /   -- + ---------                                     /             2                  /  1    I*\/ 255    | |             /             2                  /  1    I*\/ 255             /          3 /   -- + ---------                                     /             2                  /  1    I*\/ 255    | |             /          3 /   -- + ---------                                     /             2                  /  1    I*\/ 255              /             2                  /  1    I*\/ 255   |
  |          /    --------------------- + 2*3 /   -- + ---------           /           \/    16       16                                       /    --------------------- + 2*3 /   -- + ---------   | |            /    --------------------- + 2*3 /   -- + ---------           /           \/    16       16                                       /    --------------------- + 2*3 /   -- + ---------   | |            /    --------------------- + 2*3 /   -- + ---------           /           \/    16       16                                       /    --------------------- + 2*3 /   -- + ---------   | |            /           \/    16       16                                       /    --------------------- + 2*3 /   -- + ---------            /    --------------------- + 2*3 /   -- + ---------  |
  |         /          ________________     \/    16       16             /                                                                   /          ________________     \/    16       16      | |           /          ________________     \/    16       16             /                                                                   /          ________________     \/    16       16      | |           /          ________________     \/    16       16             /                                                                   /          ________________     \/    16       16      | |           /                                                                   /          ________________     \/    16       16              /          ________________     \/    16       16     |
  |        /          /          _____                                   /                                                                   /          /          _____                             | |          /          /          _____                                   /                                                                   /          /          _____                             | |          /          /          _____                                   /                                                                   /          /          _____                             | |          /                                                                   /          /          _____                                    /          /          _____                            |
  |       /          /  1    I*\/ 255                                   /                                                                   /          /  1    I*\/ 255                              | |         /          /  1    I*\/ 255                                   /                                                                   /          /  1    I*\/ 255                              | |         /          /  1    I*\/ 255                                   /                                                                   /          /  1    I*\/ 255                              | |         /                                                                   /          /  1    I*\/ 255                                    /          /  1    I*\/ 255                             |
  |      /        3 /   -- + ---------                                 /                                                                   /        3 /   -- + ---------                             | |        /        3 /   -- + ---------                                 /                                                                   /        3 /   -- + ---------                             | |        /        3 /   -- + ---------                                 /                                                                   /        3 /   -- + ---------                             | |        /                                                                   /        3 /   -- + ---------                                  /        3 /   -- + ---------                            |
  |    \/         \/    16       16                                  \/                                                                  \/         \/    16       16                                | |      \/         \/    16       16                                  \/                                                                  \/         \/    16       16                                | |      \/         \/    16       16                                  \/                                                                  \/         \/    16       16                                | |      \/                                                                  \/         \/    16       16                                   \/         \/    16       16                               |
x*|x + ----------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------|*|x + - ----------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------|*|x + - ----------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------|*|x + - -------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------|
  \                                 2                                                                                               2                                                                / \                                   2                                                                                               2                                                                / \                                   2                                                                                               2                                                                / \                                                                     2                                                                                                2                             /
x(x+(−2116+255i163+22116+255i163+2116+255i163−2116+255i1632+2116+255i163+2116+255i1632))(x+(−−2116+255i163−22116+255i163+2116+255i163−2116+255i1632−2116+255i163+2116+255i1632))(x+(−2116+255i163+2116+255i1632+−2116+255i163−22116+255i163+2116+255i163−2116+255i1632))(x+(2116+255i163+2116+255i1632−−2116+255i163+22116+255i163+2116+255i163−2116+255i1632))x \left(x + \left(\frac{\sqrt{- 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}} + \frac{2}{\sqrt{\frac{2}{\sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}}}} - \frac{2}{\sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}}}}}{2} + \frac{\sqrt{\frac{2}{\sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}} - \frac{2}{\sqrt{\frac{2}{\sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}}}} - \frac{2}{\sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}}}}}{2} - \frac{\sqrt{\frac{2}{\sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{\frac{2}{\sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}} - \frac{2}{\sqrt{\frac{2}{\sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}}}} - \frac{2}{\sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}}}}}{2}\right)\right) \left(x + \left(\frac{\sqrt{\frac{2}{\sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}}}}{2} - \frac{\sqrt{- 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}} + \frac{2}{\sqrt{\frac{2}{\sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}}}} - \frac{2}{\sqrt[3]{\frac{1}{16} + \frac{\sqrt{255} i}{16}}}}}{2}\right)\right) 
(((x*(x + sqrt(2/(1/16 + i*sqrt(255)/16)^(1/3) + 2*(1/16 + i*sqrt(255)/16)^(1/3))/2 + sqrt(-2/(1/16 + i*sqrt(255)/16)^(1/3) - 2*(1/16 + i*sqrt(255)/16)^(1/3) + 2/sqrt(2/(1/16 + i*sqrt(255)/16)^(1/3) + 2*(1/16 + i*sqrt(255)/16)^(1/3)))/2))*(x - sqrt(2/(1/16 + i*sqrt(255)/16)^(1/3) + 2*(1/16 + i*sqrt(255)/16)^(1/3))/2 - sqrt(-2/(1/16 + i*sqrt(255)/16)^(1/3) - 2*(1/16 + i*sqrt(255)/16)^(1/3) - 2/sqrt(2/(1/16 + i*sqrt(255)/16)^(1/3) + 2*(1/16 + i*sqrt(255)/16)^(1/3)))/2))*(x - sqrt(2/(1/16 + i*sqrt(255)/16)^(1/3) + 2*(1/16 + i*sqrt(255)/16)^(1/3))/2 + sqrt(-2/(1/16 + i*sqrt(255)/16)^(1/3) - 2*(1/16 + i*sqrt(255)/16)^(1/3) - 2/sqrt(2/(1/16 + i*sqrt(255)/16)^(1/3) + 2*(1/16 + i*sqrt(255)/16)^(1/3)))/2))*(x - sqrt(-2/(1/16 + i*sqrt(255)/16)^(1/3) - 2*(1/16 + i*sqrt(255)/16)^(1/3) + 2/sqrt(2/(1/16 + i*sqrt(255)/16)^(1/3) + 2*(1/16 + i*sqrt(255)/16)^(1/3)))/2 + sqrt(2/(1/16 + i*sqrt(255)/16)^(1/3) + 2*(1/16 + i*sqrt(255)/16)^(1/3))/2)
Parte trigonométrica [src] 
      3    6
 2   x    x 
x  + -- + --
     3    3
x63+x33+x2\frac{x^{6}}{3} + \frac{x^{3}}{3} + x^{2} 
x^2 + x^3/3 + x^6/3
Compilar la expresión [src] 
      3    6
 2   x    x 
x  + -- + --
     3    3
x63+x33+x2\frac{x^{6}}{3} + \frac{x^{3}}{3} + x^{2} 
x^2 + x^3/3 + x^6/3
Respuesta numérica [src] 
x^2 + 0.333333333333333*x^3 + 0.333333333333333*x^6
x^2 + 0.333333333333333*x^3 + 0.333333333333333*x^6
Denominador común [src] 
      3    6
 2   x    x 
x  + -- + --
     3    3
x63+x33+x2\frac{x^{6}}{3} + \frac{x^{3}}{3} + x^{2} 
x^2 + x^3/3 + x^6/3
Denominador racional [src] 
 3    6      2
x  + x  + 3*x 
--------------
      3
x6+x3+3x23\frac{x^{6} + x^{3} + 3 x^{2}}{3} 
(x^3 + x^6 + 3*x^2)/3
Combinatoria [src] 
 2 /         4\
x *\3 + x + x /
---------------
       3
x2(x4+x+3)3\frac{x^{2} \left(x^{4} + x + 3\right)}{3} 
x^2*(3 + x + x^4)/3
Unión de expresiones racionales [src] 
 2 /         4\
x *\3 + x + x /
---------------
       3
x2(x4+x+3)3\frac{x^{2} \left(x^{4} + x + 3\right)}{3} 
x^2*(3 + x + x^4)/3
Potencias [src] 
      3    6
 2   x    x 
x  + -- + --
     3    3
x63+x33+x2\frac{x^{6}}{3} + \frac{x^{3}}{3} + x^{2} 
x^2 + x^3/3 + x^6/3
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