Sr Examen
Factorizar el polinomio x^8-1
Solución
Factorización
[src]
/ ___ ___\ / ___ ___\ / ___ ___\ / ___ ___\
| \/ 2 I*\/ 2 | | \/ 2 I*\/ 2 | | \/ 2 I*\/ 2 | | \/ 2 I*\/ 2 |
(x + 1)*(x - 1)*(x + I)*(x - I)*|x + ----- + -------|*|x + ----- - -------|*|x + - ----- + -------|*|x + - ----- - -------|
\ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 /
$$\left(x - 1\right) \left(x + 1\right) \left(x + i\right) \left(x - i\right) \left(x + \left(\frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) \left(x + \left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right) \left(x + \left(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) \left(x + \left(- \frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right)$$
(((((((x + 1)*(x - 1))*(x + i))*(x - i))*(x + sqrt(2)/2 + i*sqrt(2)/2))*(x + sqrt(2)/2 - i*sqrt(2)/2))*(x - sqrt(2)/2 + i*sqrt(2)/2))*(x - sqrt(2)/2 - i*sqrt(2)/2)
Combinatoria
[src]
/ 2\ / 4\ (1 + x)*\1 + x /*\1 + x /*(-1 + x)
$$\left(x - 1\right) \left(x + 1\right) \left(x^{2} + 1\right) \left(x^{4} + 1\right)$$
(1 + x)*(1 + x^2)*(1 + x^4)*(-1 + x)