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Simplificación de expresiones/ Descomposición de multiplicadores/ y^5-y^3-y+1

Factorizar el polinomio y^5-y^3-y+1

Expresión a simplificar:

Solución

Ha introducido [src] 
 5    3        
y  - y  - y + 1
$$\left(- y + \left(y^{5} - y^{3}\right)\right) + 1$$ 
y^5 - y^3 - y + 1
Simplificación general [src] 
     5        3
1 + y  - y - y
$$y^{5} - y^{3} - y + 1$$ 
1 + y^5 - y - y^3
Factorización [src] 
        /                       _____________________________________________________________________________________________________________________________                                                                    \ /                                                                                           _____________________________________________________________________________________________________________________________\ /                                                                                           _____________________________________________________________________________________________________________________________\ /                                                                                           _____________________________________________________________________________________________________________________________\
        |                      /            ________________                                                                                                                                                                     | |                                                                                          /            ________________                                                                                                 | |                                                                                          /            ________________                                                                                                 | |                                                                                          /            ________________                                                                                                 |
        |                     /            /          _____                                                                                                                                                                      | |                                                                                         /            /          _____                                                                                                  | |                                                                                         /            /          _____                                                                                                  | |                                                                                         /            /          _____                                                                                                  |
        |                    /   1        /    1    \/ 849                                      1                                               2                                                                                | |                                                                                        /   1        /    1    \/ 849                                      1                                               2            | |                                                                                        /   1        /    1    \/ 849                                      1                                               2            | |                                                                                        /   1        /    1    \/ 849                                      1                                               2            |
        |                   /    - - 2*3 /   - -- + -------  + ------------------------------------------------------------------- + -----------------------                                                                     | |                                                                                       /    - - 2*3 /   - -- + -------  - ------------------------------------------------------------------- + ----------------------- | |                                                                                       /    - - 2*3 /   - -- + -------  - ------------------------------------------------------------------- + ----------------------- | |                                                                                       /    - - 2*3 /   - -- + -------  + ------------------------------------------------------------------- + ----------------------- |
        |                  /     2     \/      16     144                  _______________________________________________________          ________________              _______________________________________________________| |                  _______________________________________________________             /     2     \/      16     144                  _______________________________________________________          ________________ | |                  _______________________________________________________             /     2     \/      16     144                  _______________________________________________________          ________________ | |                  _______________________________________________________             /     2     \/      16     144                  _______________________________________________________          ________________ |
        |                 /                                               /            ________________                                    /          _____              /            ________________                           | |                 /            ________________                                       /                                               /            ________________                                    /          _____  | |                 /            ________________                                       /                                               /            ________________                                    /          _____  | |                 /            ________________                                       /                                               /            ________________                                    /          _____  |
        |                /                                               /            /          _____                                    /    1    \/ 849              /            /          _____                            | |                /            /          _____                                       /                                               /            /          _____                                    /    1    \/ 849   | |                /            /          _____                                       /                                               /            /          _____                                    /    1    \/ 849   | |                /            /          _____                                       /                                               /            /          _____                                    /    1    \/ 849   |
        |               /                                               /   1        /    1    \/ 849                2               3*3 /   - -- + -------            /   1        /    1    \/ 849                2            | |               /   1        /    1    \/ 849                2                      /                                               /   1        /    1    \/ 849                2               3*3 /   - -- + -------  | |               /   1        /    1    \/ 849                2                      /                                               /   1        /    1    \/ 849                2               3*3 /   - -- + -------  | |               /   1        /    1    \/ 849                2                      /                                               /   1        /    1    \/ 849                2               3*3 /   - -- + -------  |
        |              /                                       4*      /    - + 2*3 /   - -- + -------  - -----------------------      \/      16     144             /    - + 2*3 /   - -- + -------  - ----------------------- | |              /    - + 2*3 /   - -- + -------  - -----------------------          /                                       4*      /    - + 2*3 /   - -- + -------  - -----------------------      \/      16     144    | |              /    - + 2*3 /   - -- + -------  - -----------------------          /                                       4*      /    - + 2*3 /   - -- + -------  - -----------------------      \/      16     144    | |              /    - + 2*3 /   - -- + -------  - -----------------------          /                                       4*      /    - + 2*3 /   - -- + -------  - -----------------------      \/      16     144    |
        |             /                                               /     4     \/      16     144             ________________                                    /     4     \/      16     144             ________________ | |             /     4     \/      16     144             ________________         /                                               /     4     \/      16     144             ________________                            | |             /     4     \/      16     144             ________________         /                                               /     4     \/      16     144             ________________                            | |             /     4     \/      16     144             ________________         /                                               /     4     \/      16     144             ________________                            |
        |            /                                               /                                          /          _____                                    /                                          /          _____  | |            /                                          /          _____         /                                               /                                          /          _____                             | |            /                                          /          _____         /                                               /                                          /          _____                             | |            /                                          /          _____         /                                               /                                          /          _____                             |
        |           /                                               /                                          /    1    \/ 849                                    /                                          /    1    \/ 849   | |           /                                          /    1    \/ 849         /                                               /                                          /    1    \/ 849                              | |           /                                          /    1    \/ 849         /                                               /                                          /    1    \/ 849                              | |           /                                          /    1    \/ 849         /                                               /                                          /    1    \/ 849                              |
        |          /                                               /                                      3*3 /   - -- + -------                                  /                                      3*3 /   - -- + -------  | |          /                                      3*3 /   - -- + -------       /                                               /                                      3*3 /   - -- + -------                             | |          /                                      3*3 /   - -- + -------       /                                               /                                      3*3 /   - -- + -------                             | |          /                                      3*3 /   - -- + -------       /                                               /                                      3*3 /   - -- + -------                             |
        |    1   \/                                              \/                                         \/      16     144                                  \/                                         \/      16     144    | |    1   \/                                         \/      16     144       \/                                              \/                                         \/      16     144                               | |    1   \/                                         \/      16     144       \/                                              \/                                         \/      16     144                               | |    1   \/                                         \/      16     144       \/                                              \/                                         \/      16     144                               |
(x - 1)*|x + - - -------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------|*|x + - - ----------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------|*|x + - - ----------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------|*|x + - + ----------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------|
        \    4                                                                        2                                                                                                         2                                / \    4                                   2                                                                                                        2                                                                      / \    4                                   2                                                                                                        2                                                                      / \    4                                   2                                                                                                        2                                                                      /
$$\left(x - 1\right) \left(x + \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}} + \frac{1}{2} + \frac{2}{3 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}}} + \frac{1}{4 \sqrt{- \frac{2}{3 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}}} + \frac{1}{4} + 2 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}}}}}}{2} + \frac{\sqrt{- \frac{2}{3 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}}} + \frac{1}{4} + 2 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}}}}{2} + \frac{1}{4}\right)\right) \left(x + \left(- \frac{\sqrt{- \frac{2}{3 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}}} + \frac{1}{4} + 2 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}}}}{2} + \frac{1}{4} + \frac{\sqrt{- \frac{1}{4 \sqrt{- \frac{2}{3 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}}} + \frac{1}{4} + 2 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}}}} - 2 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}} + \frac{1}{2} + \frac{2}{3 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}}}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{- \frac{2}{3 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}}} + \frac{1}{4} + 2 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}}}}{2} + \frac{1}{4} - \frac{\sqrt{- \frac{1}{4 \sqrt{- \frac{2}{3 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}}} + \frac{1}{4} + 2 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}}}} - 2 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}} + \frac{1}{2} + \frac{2}{3 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}}}}}{2}\right)\right) \left(x + \left(\frac{\sqrt{- \frac{2}{3 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}}} + \frac{1}{4} + 2 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}}}}{2} + \frac{1}{4} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}} + \frac{1}{2} + \frac{2}{3 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}}} + \frac{1}{4 \sqrt{- \frac{2}{3 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}}} + \frac{1}{4} + 2 \sqrt[3]{- \frac{1}{16} + \frac{\sqrt{849}}{144}}}}}}{2}\right)\right)$$ 
((((x - 1)*(x + 1/4 - sqrt(1/2 - 2*(-1/16 + sqrt(849)/144)^(1/3) + 1/(4*sqrt(1/4 + 2*(-1/16 + sqrt(849)/144)^(1/3) - 2/(3*(-1/16 + sqrt(849)/144)^(1/3)))) + 2/(3*(-1/16 + sqrt(849)/144)^(1/3)))/2 + sqrt(1/4 + 2*(-1/16 + sqrt(849)/144)^(1/3) - 2/(3*(-1/16 + sqrt(849)/144)^(1/3)))/2))*(x + 1/4 - sqrt(1/4 + 2*(-1/16 + sqrt(849)/144)^(1/3) - 2/(3*(-1/16 + sqrt(849)/144)^(1/3)))/2 + sqrt(1/2 - 2*(-1/16 + sqrt(849)/144)^(1/3) - 1/(4*sqrt(1/4 + 2*(-1/16 + sqrt(849)/144)^(1/3) - 2/(3*(-1/16 + sqrt(849)/144)^(1/3)))) + 2/(3*(-1/16 + sqrt(849)/144)^(1/3)))/2))*(x + 1/4 - sqrt(1/4 + 2*(-1/16 + sqrt(849)/144)^(1/3) - 2/(3*(-1/16 + sqrt(849)/144)^(1/3)))/2 - sqrt(1/2 - 2*(-1/16 + sqrt(849)/144)^(1/3) - 1/(4*sqrt(1/4 + 2*(-1/16 + sqrt(849)/144)^(1/3) - 2/(3*(-1/16 + sqrt(849)/144)^(1/3)))) + 2/(3*(-1/16 + sqrt(849)/144)^(1/3)))/2))*(x + 1/4 + sqrt(1/4 + 2*(-1/16 + sqrt(849)/144)^(1/3) - 2/(3*(-1/16 + sqrt(849)/144)^(1/3)))/2 + sqrt(1/2 - 2*(-1/16 + sqrt(849)/144)^(1/3) + 1/(4*sqrt(1/4 + 2*(-1/16 + sqrt(849)/144)^(1/3) - 2/(3*(-1/16 + sqrt(849)/144)^(1/3)))) + 2/(3*(-1/16 + sqrt(849)/144)^(1/3)))/2)
Compilar la expresión [src] 
     5        3
1 + y  - y - y
$$y^{5} - y^{3} - y + 1$$ 
1 + y^5 - y - y^3
Denominador racional [src] 
     5        3
1 + y  - y - y
$$y^{5} - y^{3} - y + 1$$ 
1 + y^5 - y - y^3
Parte trigonométrica [src] 
     5        3
1 + y  - y - y
$$y^{5} - y^{3} - y + 1$$ 
1 + y^5 - y - y^3
Denominador común [src] 
     5        3
1 + y  - y - y
$$y^{5} - y^{3} - y + 1$$ 
1 + y^5 - y - y^3
Unión de expresiones racionales [src] 
      /      2 /      2\\
1 + y*\-1 + y *\-1 + y //
$$y \left(y^{2} \left(y^{2} - 1\right) - 1\right) + 1$$ 
1 + y*(-1 + y^2*(-1 + y^2))
Respuesta numérica [src] 
1.0 + y^5 - y - y^3
1.0 + y^5 - y - y^3
Combinatoria [src] 
         /      3    4\
(-1 + y)*\-1 + y  + y /
$$\left(y - 1\right) \left(y^{4} + y^{3} - 1\right)$$ 
(-1 + y)*(-1 + y^3 + y^4)
Potencias [src] 
     5        3
1 + y  - y - y
$$y^{5} - y^{3} - y + 1$$ 
1 + y^5 - y - y^3
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