Sr Examen
Factorizar el polinomio x^5-y^5
Solución
Factorización
[src]
/ / ___________\\ / / ___________\\ / / ___________\\ / / ___________\\
| | ___ / ___ || | | ___ / ___ || | | ___ / ___ || | | ___ / ___ ||
| | 1 \/ 5 / 5 \/ 5 || | | 1 \/ 5 / 5 \/ 5 || | | 1 \/ 5 / 5 \/ 5 || | | 1 \/ 5 / 5 \/ 5 ||
(x - y)*|x - y*|- - + ----- - I* / - + ----- ||*|x - y*|- - + ----- + I* / - + ----- ||*|x - y*|- - - ----- - I* / - - ----- ||*|x - y*|- - - ----- + I* / - - ----- ||
\ \ 4 4 \/ 8 8 // \ \ 4 4 \/ 8 8 // \ \ 4 4 \/ 8 8 // \ \ 4 4 \/ 8 8 //
$$\left(x - y\right) \left(x - y \left(- \frac{1}{4} + \frac{\sqrt{5}}{4} - i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(x - y \left(- \frac{1}{4} + \frac{\sqrt{5}}{4} + i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(x - y \left(- \frac{\sqrt{5}}{4} - \frac{1}{4} - i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(x - y \left(- \frac{\sqrt{5}}{4} - \frac{1}{4} + i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right)$$
((((x - y)*(x - y*(-1/4 + sqrt(5)/4 - i*sqrt(5/8 + sqrt(5)/8))))*(x - y*(-1/4 + sqrt(5)/4 + i*sqrt(5/8 + sqrt(5)/8))))*(x - y*(-1/4 - sqrt(5)/4 - i*sqrt(5/8 - sqrt(5)/8))))*(x - y*(-1/4 - sqrt(5)/4 + i*sqrt(5/8 - sqrt(5)/8)))
Combinatoria
[src]
/ 4 4 3 3 2 2\ (x - y)*\x + y + x*y + y*x + x *y /
$$\left(x - y\right) \left(x^{4} + x^{3} y + x^{2} y^{2} + x y^{3} + y^{4}\right)$$
(x - y)*(x^4 + y^4 + x*y^3 + y*x^3 + x^2*y^2)