Sr Examen
Factorizar el polinomio x^5-243
Solución
Factorización
[src]
/ ___________\ / ___________\ / ___________\ / ___________\
| ___ / ___ | | ___ / ___ | | ___ / ___ | | ___ / ___ |
| 3 3*\/ 5 / 5 \/ 5 | | 3 3*\/ 5 / 5 \/ 5 | | 3 3*\/ 5 / 5 \/ 5 | | 3 3*\/ 5 / 5 \/ 5 |
(x - 3)*|x + - - ------- + 3*I* / - + ----- |*|x + - - ------- - 3*I* / - + ----- |*|x + - + ------- + 3*I* / - - ----- |*|x + - + ------- - 3*I* / - - ----- |
\ 4 4 \/ 8 8 / \ 4 4 \/ 8 8 / \ 4 4 \/ 8 8 / \ 4 4 \/ 8 8 /
$$\left(x - 3\right) \left(x + \left(- \frac{3 \sqrt{5}}{4} + \frac{3}{4} + 3 i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(x + \left(- \frac{3 \sqrt{5}}{4} + \frac{3}{4} - 3 i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(x + \left(\frac{3}{4} + \frac{3 \sqrt{5}}{4} + 3 i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(x + \left(\frac{3}{4} + \frac{3 \sqrt{5}}{4} - 3 i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right)$$
((((x - 3)*(x + 3/4 - 3*sqrt(5)/4 + 3*i*sqrt(5/8 + sqrt(5)/8)))*(x + 3/4 - 3*sqrt(5)/4 - 3*i*sqrt(5/8 + sqrt(5)/8)))*(x + 3/4 + 3*sqrt(5)/4 + 3*i*sqrt(5/8 - sqrt(5)/8)))*(x + 3/4 + 3*sqrt(5)/4 - 3*i*sqrt(5/8 - sqrt(5)/8))
Combinatoria
[src]
/ 4 3 2 \ (-3 + x)*\81 + x + 3*x + 9*x + 27*x/
$$\left(x - 3\right) \left(x^{4} + 3 x^{3} + 9 x^{2} + 27 x + 81\right)$$
(-3 + x)*(81 + x^4 + 3*x^3 + 9*x^2 + 27*x)