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Factorizar el polinomio x^8+1

Expresión a simplificar:

Solución

Ha introducido [src]
 8    
x  + 1
$$x^{8} + 1$$
x^8 + 1
Factorización [src]
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|        /       ___          /       ___ | |          /       ___          /       ___ | |        /       ___          /       ___ | |          /       ___          /       ___ | |      \/ 2 *  /   - + -----    \/ 2 *  /   - - -----    I*\/ 2 *  /   - - -----    I*\/ 2 *  /   - + ----- | |      \/ 2 *  /   - - -----    \/ 2 *  /   - + -----    I*\/ 2 *  /   - - -----    I*\/ 2 *  /   - + ----- | |    \/ 2 *  /   - - -----    \/ 2 *  /   - + -----    I*\/ 2 *  /   - + -----    I*\/ 2 *  /   - - ----- | |      \/ 2 *  /   - - -----    \/ 2 *  /   - + -----    I*\/ 2 *  /   - - -----    I*\/ 2 *  /   - + ----- |
|       /  1   \/ 2          /  1   \/ 2  | |         /  1   \/ 2          /  1   \/ 2  | |       /  1   \/ 2          /  1   \/ 2  | |         /  1   \/ 2          /  1   \/ 2  | |            \/    2     4            \/    2     4              \/    2     4              \/    2     4   | |            \/    2     4            \/    2     4              \/    2     4              \/    2     4   | |          \/    2     4            \/    2     4              \/    2     4              \/    2     4   | |            \/    2     4            \/    2     4              \/    2     4              \/    2     4   |
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$$\left(x + \left(- \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} + i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}\right)\right) \left(x + \left(\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} - i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}\right)\right) \left(x + \left(\sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} + i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}\right)\right) \left(x + \left(- \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} - i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}\right)\right) \left(x + \left(- \frac{\sqrt{2} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2} + \frac{\sqrt{2} \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2} - \frac{\sqrt{2} i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2} - \frac{\sqrt{2} i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{2} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2} - \frac{\sqrt{2} \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2} - \frac{\sqrt{2} i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2} + \frac{\sqrt{2} i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2}\right)\right) \left(x + \left(\frac{\sqrt{2} \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2} + \frac{\sqrt{2} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2} - \frac{\sqrt{2} i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2} + \frac{\sqrt{2} i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{2} \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2} + \frac{\sqrt{2} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2} + \frac{\sqrt{2} i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2} + \frac{\sqrt{2} i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2}\right)\right)$$
(((((((x + sqrt(1/2 - sqrt(2)/4) - i*sqrt(1/2 + sqrt(2)/4))*(x - sqrt(1/2 - sqrt(2)/4) + i*sqrt(1/2 + sqrt(2)/4)))*(x + sqrt(1/2 + sqrt(2)/4) + i*sqrt(1/2 - sqrt(2)/4)))*(x - sqrt(1/2 + sqrt(2)/4) - i*sqrt(1/2 - sqrt(2)/4)))*(x - sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2 + sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2 - i*sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2 - i*sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2))*(x - sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2 - sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2 - i*sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2 + i*sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2))*(x + sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2 + sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2 - i*sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2 + i*sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2))*(x - sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2 + sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2 + i*sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2 + i*sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2)
Respuesta numérica [src]
1.0 + x^8
1.0 + x^8