Sr Examen
Factorizar el polinomio x^6+5*x
Solución
Factorización
[src]
/ ___________ ___________\ / ___________ ___________ ___________ ___________\ / ___________ ___________ ___________ ___________\
| / ___ / ___ | | / ___ / ___ / ___ / ___ | | / ___ / ___ / ___ / ___ |
/ ___________\ | 5 ___ / 5 \/ 5 7/10 / 5 \/ 5 | | ___________ ___________ 5 ___ / 5 \/ 5 5 ___ / 5 \/ 5 7/10 / 5 \/ 5 7/10 / 5 \/ 5 | | ___________ ___________ 5 ___ / 5 \/ 5 5 ___ / 5 \/ 5 7/10 / 5 \/ 5 7/10 / 5 \/ 5 |
| 5 ___ 7/10 / ___ | | 7/10 5 ___ I*\/ 5 * / - - ----- I*5 * / - - ----- | | 5 ___ / ___ / ___ I*\/ 5 * / - - ----- I*\/ 5 * / - + ----- I*5 * / - + ----- I*5 * / - - ----- | | 5 ___ / ___ / ___ I*\/ 5 * / - - ----- I*\/ 5 * / - + ----- I*5 * / - - ----- I*5 * / - + ----- |
/ 5 ___\ | \/ 5 5 5 ___ / 5 \/ 5 | | 5 \/ 5 \/ 8 8 \/ 8 8 | | \/ 5 5 ___ / 5 \/ 5 / 5 \/ 5 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 | | \/ 5 5 ___ / 5 \/ 5 / 5 \/ 5 \/ 8 8 \/ 8 8 \/ 8 8 \/ 8 8 |
x*\x + \/ 5 /*|x + - ----- - ----- - I*\/ 5 * / - - ----- |*|x + ----- - ----- + ------------------------ + ------------------------|*|x + - ----- - \/ 5 * / - - ----- * / - + ----- + ------------------------ + ------------------------ + ------------------------ - ------------------------|*|x + - ----- + \/ 5 * / - - ----- * / - + ----- + ------------------------ - ------------------------ - ------------------------ - ------------------------|
\ 4 4 \/ 8 8 / \ 4 4 2 2 / \ 4 \/ 8 8 \/ 8 8 4 4 4 4 / \ 4 \/ 8 8 \/ 8 8 4 4 4 4 /
$$x \left(x + \sqrt[5]{5}\right) \left(x + \left(- \frac{5^{\frac{7}{10}}}{4} - \frac{\sqrt[5]{5}}{4} - \sqrt[5]{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(x + \left(- \frac{\sqrt[5]{5}}{4} + \frac{5^{\frac{7}{10}}}{4} + \frac{\sqrt[5]{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} + \frac{5^{\frac{7}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2}\right)\right) \left(x + \left(- \sqrt[5]{5} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} - \frac{\sqrt[5]{5}}{4} - \frac{5^{\frac{7}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{4} + \frac{\sqrt[5]{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{4} + \frac{\sqrt[5]{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{4} + \frac{5^{\frac{7}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{4}\right)\right) \left(x + \left(- \frac{\sqrt[5]{5}}{4} + \sqrt[5]{5} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} - \frac{5^{\frac{7}{10}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{4} - \frac{5^{\frac{7}{10}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{4} - \frac{\sqrt[5]{5} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{4} + \frac{\sqrt[5]{5} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{4}\right)\right)$$
((((x*(x + 5^(1/5)))*(x - 5^(1/5)/4 - 5^(7/10)/4 - i*5^(1/5)*sqrt(5/8 - sqrt(5)/8)))*(x + 5^(7/10)/4 - 5^(1/5)/4 + i*5^(1/5)*sqrt(5/8 - sqrt(5)/8)/2 + i*5^(7/10)*sqrt(5/8 - sqrt(5)/8)/2))*(x - 5^(1/5)/4 - 5^(1/5)*sqrt(5/8 - sqrt(5)/8)*sqrt(5/8 + sqrt(5)/8) + i*5^(1/5)*sqrt(5/8 - sqrt(5)/8)/4 + i*5^(1/5)*sqrt(5/8 + sqrt(5)/8)/4 + i*5^(7/10)*sqrt(5/8 + sqrt(5)/8)/4 - i*5^(7/10)*sqrt(5/8 - sqrt(5)/8)/4))*(x - 5^(1/5)/4 + 5^(1/5)*sqrt(5/8 - sqrt(5)/8)*sqrt(5/8 + sqrt(5)/8) + i*5^(1/5)*sqrt(5/8 - sqrt(5)/8)/4 - i*5^(1/5)*sqrt(5/8 + sqrt(5)/8)/4 - i*5^(7/10)*sqrt(5/8 - sqrt(5)/8)/4 - i*5^(7/10)*sqrt(5/8 + sqrt(5)/8)/4)