Sr Examen

Factorizar el polinomio m^6-27

Expresión a simplificar:

Solución

Ha introducido [src]
 6     
m  - 27
$$m^{6} - 27$$
m^6 - 27
Factorización [src]
                        /            ___\ /      ___      \ /        ___      \ /        ___      \
/      ___\ /      ___\ |    3*I   \/ 3 | |    \/ 3    3*I| |      \/ 3    3*I| |      \/ 3    3*I|
\m + \/ 3 /*\m - \/ 3 /*|m + --- + -----|*|m + ----- - ---|*|m + - ----- + ---|*|m + - ----- - ---|
                        \     2      2  / \      2      2 / \        2      2 / \        2      2 /
$$\left(m - \sqrt{3}\right) \left(m + \sqrt{3}\right) \left(m + \left(\frac{\sqrt{3}}{2} + \frac{3 i}{2}\right)\right) \left(m + \left(\frac{\sqrt{3}}{2} - \frac{3 i}{2}\right)\right) \left(m + \left(- \frac{\sqrt{3}}{2} + \frac{3 i}{2}\right)\right) \left(m + \left(- \frac{\sqrt{3}}{2} - \frac{3 i}{2}\right)\right)$$
(((((m + sqrt(3))*(m - sqrt(3)))*(m + 3*i/2 + sqrt(3)/2))*(m + sqrt(3)/2 - 3*i/2))*(m - sqrt(3)/2 + 3*i/2))*(m - sqrt(3)/2 - 3*i/2)
Respuesta numérica [src]
-27.0 + m^6
-27.0 + m^6
Combinatoria [src]
/      2\ /     4      2\
\-3 + m /*\9 + m  + 3*m /
$$\left(m^{2} - 3\right) \left(m^{4} + 3 m^{2} + 9\right)$$
(-3 + m^2)*(9 + m^4 + 3*m^2)