Sr Examen
Factorizar el polinomio x^8-4
Solución
Factorización
[src]
/ 3/4 3/4\ / 3/4 3/4\ / 3/4 3/4\ / 3/4 3/4\
/ 4 ___\ / 4 ___\ / 4 ___\ / 4 ___\ | 2 I*2 | | 2 I*2 | | 2 I*2 | | 2 I*2 |
\x + \/ 2 /*\x - \/ 2 /*\x + I*\/ 2 /*\x - I*\/ 2 /*|x + ---- + ------|*|x + ---- - ------|*|x + - ---- + ------|*|x + - ---- - ------|
\ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 /
$$\left(x - \sqrt[4]{2}\right) \left(x + \sqrt[4]{2}\right) \left(x + \sqrt[4]{2} i\right) \left(x - \sqrt[4]{2} i\right) \left(x + \left(\frac{2^{\frac{3}{4}}}{2} + \frac{2^{\frac{3}{4}} i}{2}\right)\right) \left(x + \left(\frac{2^{\frac{3}{4}}}{2} - \frac{2^{\frac{3}{4}} i}{2}\right)\right) \left(x + \left(- \frac{2^{\frac{3}{4}}}{2} + \frac{2^{\frac{3}{4}} i}{2}\right)\right) \left(x + \left(- \frac{2^{\frac{3}{4}}}{2} - \frac{2^{\frac{3}{4}} i}{2}\right)\right)$$
(((((((x + 2^(1/4))*(x - 2^(1/4)))*(x + i*2^(1/4)))*(x - i*2^(1/4)))*(x + 2^(3/4)/2 + i*2^(3/4)/2))*(x + 2^(3/4)/2 - i*2^(3/4)/2))*(x - 2^(3/4)/2 + i*2^(3/4)/2))*(x - 2^(3/4)/2 - i*2^(3/4)/2)
Combinatoria
[src]
/ 4\ / 4\ \-2 + x /*\2 + x /
$$\left(x^{4} - 2\right) \left(x^{4} + 2\right)$$
(-2 + x^4)*(2 + x^4)