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Simplificación de expresiones/ Descomposición de multiplicadores/ a^5+a+1

Factorizar el polinomio a^5+a+1

Expresión a simplificar:

Solución

Ha introducido [src] 
 5        
a  + a + 1
(a5+a)+1\left(a^{5} + a\right) + 1 
a^5 + a + 1
Simplificación general [src] 
         5
1 + a + a
a5+a+1a^{5} + a + 1 
1 + a + a^5
Factorización [src] 
                                    /                                                        _______________                \ /                                                        _______________                \ /                                        _______________\
                                    |                                                       /          ____  /          ___\| |                                                       /          ____  /          ___\| |                                       /          ____ |
                                    |                                                      /  25   3*\/ 69   |  1   I*\/ 3 || |                                                      /  25   3*\/ 69   |  1   I*\/ 3 || |                                      /  25   3*\/ 69  |
/            ___\ /            ___\ |                                                   3 /   -- + -------- *|- - - -------|| |                                                   3 /   -- + -------- *|- - + -------|| |                                   3 /   -- + -------- |
|    1   I*\/ 3 | |    1   I*\/ 3 | |      1                     1                      \/    2       2      \  2      2   /| |      1                     1                      \/    2       2      \  2      2   /| |      1             1              \/    2       2     |
|a + - + -------|*|a + - - -------|*|a + - - + -------------------------------------- + ------------------------------------|*|a + - - + -------------------------------------- + ------------------------------------|*|a + - - + ---------------------- + --------------------|
\    2      2   / \    2      2   / |      3                          _______________                    3                  | |      3                          _______________                    3                  | |      3          _______________            3          |
                                    |            /          ___\     /          ____                                        | |            /          ___\     /          ____                                        | |                /          ____                        |
                                    |            |  1   I*\/ 3 |    /  25   3*\/ 69                                         | |            |  1   I*\/ 3 |    /  25   3*\/ 69                                         | |               /  25   3*\/ 69                         |
                                    |          3*|- - - -------|*3 /   -- + --------                                        | |          3*|- - + -------|*3 /   -- + --------                                        | |          3*3 /   -- + --------                        |
                                    \            \  2      2   / \/    2       2                                            / \            \  2      2   / \/    2       2                                            / \            \/    2       2                            /
(a+(12−3i2))(a+(12+3i2))(a+(−13+(−12−3i2)3692+25233+13(−12−3i2)3692+2523))(a+(−13+13(−12+3i2)3692+2523+(−12+3i2)3692+25233))(a+(−13+133692+2523+3692+25233))\left(a + \left(\frac{1}{2} - \frac{\sqrt{3} i}{2}\right)\right) \left(a + \left(\frac{1}{2} + \frac{\sqrt{3} i}{2}\right)\right) \left(a + \left(- \frac{1}{3} + \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{69}}{2} + \frac{25}{2}}}{3} + \frac{1}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{69}}{2} + \frac{25}{2}}}\right)\right) \left(a + \left(- \frac{1}{3} + \frac{1}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{69}}{2} + \frac{25}{2}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{69}}{2} + \frac{25}{2}}}{3}\right)\right) \left(a + \left(- \frac{1}{3} + \frac{1}{3 \sqrt[3]{\frac{3 \sqrt{69}}{2} + \frac{25}{2}}} + \frac{\sqrt[3]{\frac{3 \sqrt{69}}{2} + \frac{25}{2}}}{3}\right)\right) 
((((a + 1/2 + i*sqrt(3)/2)*(a + 1/2 - i*sqrt(3)/2))*(a - 1/3 + 1/(3*(-1/2 - i*sqrt(3)/2)*(25/2 + 3*sqrt(69)/2)^(1/3)) + (25/2 + 3*sqrt(69)/2)^(1/3)*(-1/2 - i*sqrt(3)/2)/3))*(a - 1/3 + 1/(3*(-1/2 + i*sqrt(3)/2)*(25/2 + 3*sqrt(69)/2)^(1/3)) + (25/2 + 3*sqrt(69)/2)^(1/3)*(-1/2 + i*sqrt(3)/2)/3))*(a - 1/3 + 1/(3*(25/2 + 3*sqrt(69)/2)^(1/3)) + (25/2 + 3*sqrt(69)/2)^(1/3)/3)
Potencias [src] 
         5
1 + a + a
a5+a+1a^{5} + a + 1 
1 + a + a^5
Combinatoria [src] 
/         2\ /     3    2\
\1 + a + a /*\1 + a  - a /
(a2+a+1)(a3−a2+1)\left(a^{2} + a + 1\right) \left(a^{3} - a^{2} + 1\right) 
(1 + a + a^2)*(1 + a^3 - a^2)
Parte trigonométrica [src] 
         5
1 + a + a
a5+a+1a^{5} + a + 1 
1 + a + a^5
Respuesta numérica [src] 
1.0 + a + a^5
1.0 + a + a^5
Denominador racional [src] 
         5
1 + a + a
a5+a+1a^{5} + a + 1 
1 + a + a^5
Unión de expresiones racionales [src] 
      /     4\
1 + a*\1 + a /
a(a4+1)+1a \left(a^{4} + 1\right) + 1 
1 + a*(1 + a^4)
Compilar la expresión [src] 
         5
1 + a + a
a5+a+1a^{5} + a + 1 
1 + a + a^5
Denominador común [src] 
         5
1 + a + a
a5+a+1a^{5} + a + 1 
1 + a + a^5
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