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

Factorizar el polinomio a^5+a^3-a^2

Expresión a simplificar:

Solución

Ha introducido [src] 
 5    3    2
a  + a  - a
−a2+(a5+a3)- a^{2} + \left(a^{5} + a^{3}\right) 
a^5 + a^3 - a^2
Factorización [src] 
  /           ____________                                                      \ /           ____________                                                      \ /           ____________                      \
  |          /       ____  /          ___\                                      | |          /       ____  /          ___\                                      | |          /       ____                       |
  |         /  1   \/ 93   |  1   I*\/ 3 |                    1                 | |         /  1   \/ 93   |  1   I*\/ 3 |                    1                 | |         /  1   \/ 93              1         |
a*|a + - 3 /   - + ------ *|- - - -------| + -----------------------------------|*|a + - 3 /   - + ------ *|- - + -------| + -----------------------------------|*|a + - 3 /   - + ------  + -------------------|
  |      \/    2     18    \  2      2   /          ____________                | |      \/    2     18    \  2      2   /          ____________                | |      \/    2     18             ____________|
  |                                                /       ____  /          ___\| |                                                /       ____  /          ___\| |                                /       ____ |
  |                                               /  1   \/ 93   |  1   I*\/ 3 || |                                               /  1   \/ 93   |  1   I*\/ 3 || |                               /  1   \/ 93  |
  |                                          3*3 /   - + ------ *|- - - -------|| |                                          3*3 /   - + ------ *|- - + -------|| |                          3*3 /   - + ------ |
  \                                            \/    2     18    \  2      2   // \                                            \/    2     18    \  2      2   // \                            \/    2     18   /
a(a+(13(−12−3i2)12+93183−(−12−3i2)12+93183))(a+(−(−12+3i2)12+93183+13(−12+3i2)12+93183))(a+(−12+93183+1312+93183))a \left(a + \left(\frac{1}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{93}}{18}}} - \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{93}}{18}}\right)\right) \left(a + \left(- \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{93}}{18}} + \frac{1}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{93}}{18}}}\right)\right) \left(a + \left(- \sqrt[3]{\frac{1}{2} + \frac{\sqrt{93}}{18}} + \frac{1}{3 \sqrt[3]{\frac{1}{2} + \frac{\sqrt{93}}{18}}}\right)\right) 
((a*(a - (1/2 + sqrt(93)/18)^(1/3)*(-1/2 - i*sqrt(3)/2) + 1/(3*(1/2 + sqrt(93)/18)^(1/3)*(-1/2 - i*sqrt(3)/2))))*(a - (1/2 + sqrt(93)/18)^(1/3)*(-1/2 + i*sqrt(3)/2) + 1/(3*(1/2 + sqrt(93)/18)^(1/3)*(-1/2 + i*sqrt(3)/2))))*(a - (1/2 + sqrt(93)/18)^(1/3) + 1/(3*(1/2 + sqrt(93)/18)^(1/3)))
Simplificación general [src] 
 2 /          3\
a *\-1 + a + a /
a2(a3+a−1)a^{2} \left(a^{3} + a - 1\right) 
a^2*(-1 + a + a^3)
Potencias [src] 
 3    5    2
a  + a  - a
a5+a3−a2a^{5} + a^{3} - a^{2} 
a^3 + a^5 - a^2
Respuesta numérica [src] 
a^3 + a^5 - a^2
a^3 + a^5 - a^2
Denominador común [src] 
 3    5    2
a  + a  - a
a5+a3−a2a^{5} + a^{3} - a^{2} 
a^3 + a^5 - a^2
Compilar la expresión [src] 
 3    5    2
a  + a  - a
a5+a3−a2a^{5} + a^{3} - a^{2} 
a^3 + a^5 - a^2
Parte trigonométrica [src] 
 3    5    2
a  + a  - a
a5+a3−a2a^{5} + a^{3} - a^{2} 
a^3 + a^5 - a^2
Unión de expresiones racionales [src] 
 2 /       /     2\\
a *\-1 + a*\1 + a //
a2(a(a2+1)−1)a^{2} \left(a \left(a^{2} + 1\right) - 1\right) 
a^2*(-1 + a*(1 + a^2))
Denominador racional [src] 
 3    5    2
a  + a  - a
a5+a3−a2a^{5} + a^{3} - a^{2} 
a^3 + a^5 - a^2
Combinatoria [src] 
 2 /          3\
a *\-1 + a + a /
a2(a3+a−1)a^{2} \left(a^{3} + a - 1\right) 
a^2*(-1 + a + a^3)
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