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Simplificación de expresiones/ Descomposición de multiplicadores/ z^3-19*z^2/10-z/5+1/10

Factorizar el polinomio z^3-19*z^2/10-z/5+1/10

Expresión a simplificar:

Solución

Ha introducido [src] 
         2         
 3   19*z    z   1 
z  - ----- - - + --
       10    5   10
(−z5+(z3−19z210))+110\left(- \frac{z}{5} + \left(z^{3} - \frac{19 z^{2}}{10}\right)\right) + \frac{1}{10} 
z^3 - 19*z^2/10 - z/5 + 1/10
Simplificación general [src] 
              2    
1     3   19*z    z
-- + z  - ----- - -
10          10    5
z3−19z210−z5+110z^{3} - \frac{19 z^{2}}{10} - \frac{z}{5} + \frac{1}{10} 
1/10 + z^3 - 19*z^2/10 - z/5
Factorización [src] 
/                _____________________                                                                 \ /                _____________________                                                                 \ /                _____________________                                 \
|               /             _______  /          ___\                                                 | |               /             _______  /          ___\                                                 | |               /             _______                                  |
|      19      /   7219   I*\/ 25005   |  1   I*\/ 3 |                        421                      | |      19      /   7219   I*\/ 25005   |  1   I*\/ 3 |                        421                      | |      19      /   7219   I*\/ 25005                  421              |
|x + - -- - 3 /   ----- + ----------- *|- - - -------| - ----------------------------------------------|*|x + - -- - 3 /   ----- + ----------- *|- - + -------| - ----------------------------------------------|*|x + - -- - 3 /   ----- + -----------  - ------------------------------|
|      30   \/    27000       900      \  2      2   /                            _____________________| |      30   \/    27000       900      \  2      2   /                            _____________________| |      30   \/    27000       900                 _____________________|
|                                                            /          ___\     /             _______ | |                                                            /          ___\     /             _______ | |                                                /             _______ |
|                                                            |  1   I*\/ 3 |    /   7219   I*\/ 25005  | |                                                            |  1   I*\/ 3 |    /   7219   I*\/ 25005  | |                                               /   7219   I*\/ 25005  |
|                                                        900*|- - - -------|*3 /   ----- + ----------- | |                                                        900*|- - + -------|*3 /   ----- + ----------- | |                                        900*3 /   ----- + ----------- |
\                                                            \  2      2   / \/    27000       900     / \                                                            \  2      2   / \/    27000       900     / \                                            \/    27000       900     /
(x+(−1930−421900(−12−3i2)721927000+25005i9003−(−12−3i2)721927000+25005i9003))(x+(−1930−(−12+3i2)721927000+25005i9003−421900(−12+3i2)721927000+25005i9003))(x+(−1930−721927000+25005i9003−421900721927000+25005i9003))\left(x + \left(- \frac{19}{30} - \frac{421}{900 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{7219}{27000} + \frac{\sqrt{25005} i}{900}}} - \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{7219}{27000} + \frac{\sqrt{25005} i}{900}}\right)\right) \left(x + \left(- \frac{19}{30} - \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{7219}{27000} + \frac{\sqrt{25005} i}{900}} - \frac{421}{900 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{7219}{27000} + \frac{\sqrt{25005} i}{900}}}\right)\right) \left(x + \left(- \frac{19}{30} - \sqrt[3]{\frac{7219}{27000} + \frac{\sqrt{25005} i}{900}} - \frac{421}{900 \sqrt[3]{\frac{7219}{27000} + \frac{\sqrt{25005} i}{900}}}\right)\right) 
((x - 19/30 - (7219/27000 + i*sqrt(25005)/900)^(1/3)*(-1/2 - i*sqrt(3)/2) - 421/(900*(-1/2 - i*sqrt(3)/2)*(7219/27000 + i*sqrt(25005)/900)^(1/3)))*(x - 19/30 - (7219/27000 + i*sqrt(25005)/900)^(1/3)*(-1/2 + i*sqrt(3)/2) - 421/(900*(-1/2 + i*sqrt(3)/2)*(7219/27000 + i*sqrt(25005)/900)^(1/3))))*(x - 19/30 - (7219/27000 + i*sqrt(25005)/900)^(1/3) - 421/(900*(7219/27000 + i*sqrt(25005)/900)^(1/3)))
Descomposición de una fracción [src] 
1/10 + z^3 - 19*z^2/10 - z/5
z3−19z210−z5+110z^{3} - \frac{19 z^{2}}{10} - \frac{z}{5} + \frac{1}{10} 
              2    
1     3   19*z    z
-- + z  - ----- - -
10          10    5
Parte trigonométrica [src] 
              2    
1     3   19*z    z
-- + z  - ----- - -
10          10    5
z3−19z210−z5+110z^{3} - \frac{19 z^{2}}{10} - \frac{z}{5} + \frac{1}{10} 
1/10 + z^3 - 19*z^2/10 - z/5
Combinatoria [src] 
              2    
1     3   19*z    z
-- + z  - ----- - -
10          10    5
z3−19z210−z5+110z^{3} - \frac{19 z^{2}}{10} - \frac{z}{5} + \frac{1}{10} 
1/10 + z^3 - 19*z^2/10 - z/5
Denominador racional [src] 
          2                3
50 - 950*z  - 100*z + 500*z 
----------------------------
            500
500z3−950z2−100z+50500\frac{500 z^{3} - 950 z^{2} - 100 z + 50}{500} 
(50 - 950*z^2 - 100*z + 500*z^3)/500
Unión de expresiones racionales [src] 
1 + z*(-2 + z*(-19 + 10*z))
---------------------------
             10
z(z(10z−19)−2)+110\frac{z \left(z \left(10 z - 19\right) - 2\right) + 1}{10} 
(1 + z*(-2 + z*(-19 + 10*z)))/10
Compilar la expresión [src] 
              2    
1     3   19*z    z
-- + z  - ----- - -
10          10    5
z3−19z210−z5+110z^{3} - \frac{19 z^{2}}{10} - \frac{z}{5} + \frac{1}{10} 
1/10 + z^3 - 19*z^2/10 - z/5
Respuesta numérica [src] 
0.1 + z^3 - 0.2*z - 1.9*z^2
0.1 + z^3 - 0.2*z - 1.9*z^2
Potencias [src] 
              2    
1     3   19*z    z
-- + z  - ----- - -
10          10    5
z3−19z210−z5+110z^{3} - \frac{19 z^{2}}{10} - \frac{z}{5} + \frac{1}{10} 
1/10 + z^3 - 19*z^2/10 - z/5
Denominador común [src] 
              2    
1     3   19*z    z
-- + z  - ----- - -
10          10    5
z3−19z210−z5+110z^{3} - \frac{19 z^{2}}{10} - \frac{z}{5} + \frac{1}{10} 
1/10 + z^3 - 19*z^2/10 - z/5
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