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Simplificación de expresiones/ Descomposición de multiplicadores/ x^5-243

Factorizar el polinomio x^5-243

Expresión a simplificar:

Solución

Ha introducido [src] 
 5      
x  - 243
x5−243x^{5} - 243 
x^5 - 243
Factorización [src] 
        /                           ___________\ /                           ___________\ /                           ___________\ /                           ___________\
        |            ___           /       ___ | |            ___           /       ___ | |            ___           /       ___ | |            ___           /       ___ |
        |    3   3*\/ 5           /  5   \/ 5  | |    3   3*\/ 5           /  5   \/ 5  | |    3   3*\/ 5           /  5   \/ 5  | |    3   3*\/ 5           /  5   \/ 5  |
(x - 3)*|x + - - ------- + 3*I*  /   - + ----- |*|x + - - ------- - 3*I*  /   - + ----- |*|x + - + ------- + 3*I*  /   - - ----- |*|x + - + ------- - 3*I*  /   - - ----- |
        \    4      4          \/    8     8   / \    4      4          \/    8     8   / \    4      4          \/    8     8   / \    4      4          \/    8     8   /
(x−3)(x+(−354+34+3i58+58))(x+(−354+34−3i58+58))(x+(34+354+3i58−58))(x+(34+354−3i58−58))\left(x - 3\right) \left(x + \left(- \frac{3 \sqrt{5}}{4} + \frac{3}{4} + 3 i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(x + \left(- \frac{3 \sqrt{5}}{4} + \frac{3}{4} - 3 i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(x + \left(\frac{3}{4} + \frac{3 \sqrt{5}}{4} + 3 i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(x + \left(\frac{3}{4} + \frac{3 \sqrt{5}}{4} - 3 i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) 
((((x - 3)*(x + 3/4 - 3*sqrt(5)/4 + 3*i*sqrt(5/8 + sqrt(5)/8)))*(x + 3/4 - 3*sqrt(5)/4 - 3*i*sqrt(5/8 + sqrt(5)/8)))*(x + 3/4 + 3*sqrt(5)/4 + 3*i*sqrt(5/8 - sqrt(5)/8)))*(x + 3/4 + 3*sqrt(5)/4 - 3*i*sqrt(5/8 - sqrt(5)/8))
Respuesta numérica [src] 
-243.0 + x^5
-243.0 + x^5
Combinatoria [src] 
         /      4      3      2       \
(-3 + x)*\81 + x  + 3*x  + 9*x  + 27*x/
(x−3)(x4+3x3+9x2+27x+81)\left(x - 3\right) \left(x^{4} + 3 x^{3} + 9 x^{2} + 27 x + 81\right) 
(-3 + x)*(81 + x^4 + 3*x^3 + 9*x^2 + 27*x)
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