Sr Examen
Factorizar el polinomio a^6+b^3
Solución
Factorización
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/ _____ _____\ / _____ _____\ / _____ _____\ / _____ _____\
/ _____\ / _____\ | 6 / 3 ___ 6 / 3 | | 6 / 3 ___ 6 / 3 | | 6 / 3 ___ 6 / 3 | | 6 / 3 ___ 6 / 3 |
| 6 / 3 | | 6 / 3 | | \/ -b I*\/ 3 *\/ -b | | \/ -b I*\/ 3 *\/ -b | | \/ -b I*\/ 3 *\/ -b | | \/ -b I*\/ 3 *\/ -b |
\a + \/ -b /*\a - \/ -b /*|a + -------- + ----------------|*|a + -------- - ----------------|*|a + - -------- + ----------------|*|a + - -------- - ----------------|
\ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 /
$$\left(a - \sqrt[6]{- b^{3}}\right) \left(a + \sqrt[6]{- b^{3}}\right) \left(a + \left(\frac{\sqrt[6]{- b^{3}}}{2} + \frac{\sqrt{3} i \sqrt[6]{- b^{3}}}{2}\right)\right) \left(a + \left(\frac{\sqrt[6]{- b^{3}}}{2} - \frac{\sqrt{3} i \sqrt[6]{- b^{3}}}{2}\right)\right) \left(a + \left(- \frac{\sqrt[6]{- b^{3}}}{2} + \frac{\sqrt{3} i \sqrt[6]{- b^{3}}}{2}\right)\right) \left(a + \left(- \frac{\sqrt[6]{- b^{3}}}{2} - \frac{\sqrt{3} i \sqrt[6]{- b^{3}}}{2}\right)\right)$$
(((((a + (-b^3)^(1/6))*(a - (-b^3)^(1/6)))*(a + (-b^3)^(1/6)/2 + i*sqrt(3)*(-b^3)^(1/6)/2))*(a + (-b^3)^(1/6)/2 - i*sqrt(3)*(-b^3)^(1/6)/2))*(a - (-b^3)^(1/6)/2 + i*sqrt(3)*(-b^3)^(1/6)/2))*(a - (-b^3)^(1/6)/2 - i*sqrt(3)*(-b^3)^(1/6)/2)
Combinatoria
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/ 2\ / 4 2 2\ \b + a /*\a + b - b*a /
$$\left(a^{2} + b\right) \left(a^{4} - a^{2} b + b^{2}\right)$$
(b + a^2)*(a^4 + b^2 - b*a^2)