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