Sr Examen
Factorizar el polinomio 8*m^7-6*m^2*n-12*m^5*n^3+9*n^4
Solución
Ha introducido
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7 2 5 3 4 8*m - 6*m *n - 12*m *n + 9*n
$$9 n^{4} + \left(- 12 m^{5} n^{3} + \left(8 m^{7} - 6 m^{2} n\right)\right)$$
8*m^7 - 6*m^2*n - 12*m^5*n^3 + 9*n^4
Simplificación general
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7 4 5 3 2 8*m + 9*n - 12*m *n - 6*n*m
$$8 m^{7} - 12 m^{5} n^{3} - 6 m^{2} n + 9 n^{4}$$
8*m^7 + 9*n^4 - 12*m^5*n^3 - 6*n*m^2
Factorización
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/ ___________\ / ___________\ / ___________\ / ___________\
| / ___ | | / ___ | | / ___ | | / ___ |
/ ____\ / ____\ | 3/5 5 ___ 5 ___ / 5 \/ 5 | | 3/5 5 ___ 5 ___ / 5 \/ 5 | | 3/5 5 ___ 5 ___ / 5 \/ 5 | | 3/5 5 ___ 5 ___ / 5 \/ 5 |
| ___ / 3 | | ___ / 3 | / 3/5 5 ___ 5 ___\ | 3/5 5 ___ 5 ___ 3/5 5 ___ ___ 5 ___ I*2 *\/ 3 *\/ n * / - + ----- | | 3/5 5 ___ 5 ___ 3/5 5 ___ ___ 5 ___ I*2 *\/ 3 *\/ n * / - + ----- | | 3/5 5 ___ 5 ___ 3/5 5 ___ ___ 5 ___ I*2 *\/ 3 *\/ n * / - - ----- | | 3/5 5 ___ 5 ___ 3/5 5 ___ ___ 5 ___ I*2 *\/ 3 *\/ n * / - - ----- |
| \/ 6 *\/ n | | \/ 6 *\/ n | | 2 *\/ 3 *\/ n | | 2 *\/ 3 *\/ n 2 *\/ 3 *\/ 5 *\/ n \/ 8 8 | | 2 *\/ 3 *\/ n 2 *\/ 3 *\/ 5 *\/ n \/ 8 8 | | 2 *\/ 3 *\/ n 2 *\/ 3 *\/ 5 *\/ n \/ 8 8 | | 2 *\/ 3 *\/ n 2 *\/ 3 *\/ 5 *\/ n \/ 8 8 |
|m + -------------|*|m - -------------|*|m - ----------------|*|m + ---------------- - ---------------------- + -----------------------------------|*|m + ---------------- - ---------------------- - -----------------------------------|*|m + ---------------- + ---------------------- + -----------------------------------|*|m + ---------------- + ---------------------- - -----------------------------------|
\ 2 / \ 2 / \ 2 / \ 8 8 2 / \ 8 8 2 / \ 8 8 2 / \ 8 8 2 /
$$\left(m - \frac{\sqrt{6} \sqrt{n^{3}}}{2}\right) \left(m + \frac{\sqrt{6} \sqrt{n^{3}}}{2}\right) \left(m - \frac{2^{\frac{3}{5}} \sqrt[5]{3} \sqrt[5]{n}}{2}\right) \left(m + \left(- \frac{2^{\frac{3}{5}} \sqrt[5]{3} \sqrt{5} \sqrt[5]{n}}{8} + \frac{2^{\frac{3}{5}} \sqrt[5]{3} \sqrt[5]{n}}{8} + \frac{2^{\frac{3}{5}} \sqrt[5]{3} i \sqrt[5]{n} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2}\right)\right) \left(m + \left(- \frac{2^{\frac{3}{5}} \sqrt[5]{3} \sqrt{5} \sqrt[5]{n}}{8} + \frac{2^{\frac{3}{5}} \sqrt[5]{3} \sqrt[5]{n}}{8} - \frac{2^{\frac{3}{5}} \sqrt[5]{3} i \sqrt[5]{n} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2}\right)\right) \left(m + \left(\frac{2^{\frac{3}{5}} \sqrt[5]{3} \sqrt[5]{n}}{8} + \frac{2^{\frac{3}{5}} \sqrt[5]{3} \sqrt{5} \sqrt[5]{n}}{8} + \frac{2^{\frac{3}{5}} \sqrt[5]{3} i \sqrt[5]{n} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2}\right)\right) \left(m + \left(\frac{2^{\frac{3}{5}} \sqrt[5]{3} \sqrt[5]{n}}{8} + \frac{2^{\frac{3}{5}} \sqrt[5]{3} \sqrt{5} \sqrt[5]{n}}{8} - \frac{2^{\frac{3}{5}} \sqrt[5]{3} i \sqrt[5]{n} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2}\right)\right)$$
((((((m + sqrt(6)*sqrt(n^3)/2)*(m - sqrt(6)*sqrt(n^3)/2))*(m - 2^(3/5)*3^(1/5)*n^(1/5)/2))*(m + 2^(3/5)*3^(1/5)*n^(1/5)/8 - 2^(3/5)*3^(1/5)*sqrt(5)*n^(1/5)/8 + i*2^(3/5)*3^(1/5)*n^(1/5)*sqrt(5/8 + sqrt(5)/8)/2))*(m + 2^(3/5)*3^(1/5)*n^(1/5)/8 - 2^(3/5)*3^(1/5)*sqrt(5)*n^(1/5)/8 - i*2^(3/5)*3^(1/5)*n^(1/5)*sqrt(5/8 + sqrt(5)/8)/2))*(m + 2^(3/5)*3^(1/5)*n^(1/5)/8 + 2^(3/5)*3^(1/5)*sqrt(5)*n^(1/5)/8 + i*2^(3/5)*3^(1/5)*n^(1/5)*sqrt(5/8 - sqrt(5)/8)/2))*(m + 2^(3/5)*3^(1/5)*n^(1/5)/8 + 2^(3/5)*3^(1/5)*sqrt(5)*n^(1/5)/8 - i*2^(3/5)*3^(1/5)*n^(1/5)*sqrt(5/8 - sqrt(5)/8)/2)
Denominador común
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7 4 5 3 2 8*m + 9*n - 12*m *n - 6*n*m
$$8 m^{7} - 12 m^{5} n^{3} - 6 m^{2} n + 9 n^{4}$$
8*m^7 + 9*n^4 - 12*m^5*n^3 - 6*n*m^2
Respuesta numérica
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8.0*m^7 + 9.0*n^4 - 6.0*n*m^2 - 12.0*m^5*n^3
8.0*m^7 + 9.0*n^4 - 6.0*n*m^2 - 12.0*m^5*n^3
Combinatoria
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/ 5\ / 3 2\ \-3*n + 4*m /*\- 3*n + 2*m /
$$\left(2 m^{2} - 3 n^{3}\right) \left(4 m^{5} - 3 n\right)$$
(-3*n + 4*m^5)*(-3*n^3 + 2*m^2)
Unión de expresiones racionales
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4 2 / 5 3 3\ 9*n + 2*m *\-3*n + 4*m - 6*m *n /
$$2 m^{2} \left(4 m^{5} - 6 m^{3} n^{3} - 3 n\right) + 9 n^{4}$$
9*n^4 + 2*m^2*(-3*n + 4*m^5 - 6*m^3*n^3)
Parte trigonométrica
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7 4 5 3 2 8*m + 9*n - 12*m *n - 6*n*m
$$8 m^{7} - 12 m^{5} n^{3} - 6 m^{2} n + 9 n^{4}$$
8*m^7 + 9*n^4 - 12*m^5*n^3 - 6*n*m^2
Compilar la expresión
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7 4 5 3 2 8*m + 9*n - 12*m *n - 6*n*m
$$8 m^{7} - 12 m^{5} n^{3} - 6 m^{2} n + 9 n^{4}$$
8*m^7 + 9*n^4 - 12*m^5*n^3 - 6*n*m^2
Denominador racional
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7 4 5 3 2 8*m + 9*n - 12*m *n - 6*n*m
$$8 m^{7} - 12 m^{5} n^{3} - 6 m^{2} n + 9 n^{4}$$
8*m^7 + 9*n^4 - 12*m^5*n^3 - 6*n*m^2
Potencias
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7 4 5 3 2 8*m + 9*n - 12*m *n - 6*n*m
$$8 m^{7} - 12 m^{5} n^{3} - 6 m^{2} n + 9 n^{4}$$
8*m^7 + 9*n^4 - 12*m^5*n^3 - 6*n*m^2