Sr Examen
Factorizar el polinomio x^5-x^4-x^3-x^2-x-2
Solución
Ha introducido
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5 4 3 2 x - x - x - x - x - 2
$$\left(- x + \left(- x^{2} + \left(- x^{3} + \left(x^{5} - x^{4}\right)\right)\right)\right) - 2$$
x^5 - x^4 - x^3 - x^2 - x - 2
Simplificación general
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5 2 3 4 -2 + x - x - x - x - x
$$x^{5} - x^{4} - x^{3} - x^{2} - x - 2$$
-2 + x^5 - x - x^2 - x^3 - x^4
Factorización
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/ ___________\ / ___________\ / ___________\ / ___________\
| ___ / ___ | | ___ / ___ | | ___ / ___ | | ___ / ___ |
| 1 \/ 5 / 5 \/ 5 | | 1 \/ 5 / 5 \/ 5 | | 1 \/ 5 / 5 \/ 5 | | 1 \/ 5 / 5 \/ 5 |
(x - 2)*|x + - - ----- + I* / - + ----- |*|x + - - ----- - I* / - + ----- |*|x + - + ----- + I* / - - ----- |*|x + - + ----- - I* / - - ----- |
\ 4 4 \/ 8 8 / \ 4 4 \/ 8 8 / \ 4 4 \/ 8 8 / \ 4 4 \/ 8 8 /
$$\left(x - 2\right) \left(x + \left(- \frac{\sqrt{5}}{4} + \frac{1}{4} + i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(x + \left(- \frac{\sqrt{5}}{4} + \frac{1}{4} - i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(x + \left(\frac{1}{4} + \frac{\sqrt{5}}{4} + i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(x + \left(\frac{1}{4} + \frac{\sqrt{5}}{4} - i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right)$$
((((x - 2)*(x + 1/4 - sqrt(5)/4 + i*sqrt(5/8 + sqrt(5)/8)))*(x + 1/4 - sqrt(5)/4 - i*sqrt(5/8 + sqrt(5)/8)))*(x + 1/4 + sqrt(5)/4 + i*sqrt(5/8 - sqrt(5)/8)))*(x + 1/4 + sqrt(5)/4 - i*sqrt(5/8 - sqrt(5)/8))
Unión de expresiones racionales
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-2 + x*(-1 + x*(-1 + x*(-1 + x*(-1 + x))))
$$x \left(x \left(x \left(x \left(x - 1\right) - 1\right) - 1\right) - 1\right) - 2$$
-2 + x*(-1 + x*(-1 + x*(-1 + x*(-1 + x))))
Combinatoria
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/ 2 3 4\ (-2 + x)*\1 + x + x + x + x /
$$\left(x - 2\right) \left(x^{4} + x^{3} + x^{2} + x + 1\right)$$
(-2 + x)*(1 + x + x^2 + x^3 + x^4)
Parte trigonométrica
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5 2 3 4 -2 + x - x - x - x - x
$$x^{5} - x^{4} - x^{3} - x^{2} - x - 2$$
-2 + x^5 - x - x^2 - x^3 - x^4
Potencias
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5 2 3 4 -2 + x - x - x - x - x
$$x^{5} - x^{4} - x^{3} - x^{2} - x - 2$$
-2 + x^5 - x - x^2 - x^3 - x^4
Compilar la expresión
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5 2 3 4 -2 + x - x - x - x - x
$$x^{5} - x^{4} - x^{3} - x^{2} - x - 2$$
-2 + x^5 - x - x^2 - x^3 - x^4
Denominador racional
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5 2 3 4 -2 + x - x - x - x - x
$$x^{5} - x^{4} - x^{3} - x^{2} - x - 2$$
-2 + x^5 - x - x^2 - x^3 - x^4
Denominador común
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5 2 3 4 -2 + x - x - x - x - x
$$x^{5} - x^{4} - x^{3} - x^{2} - x - 2$$
-2 + x^5 - x - x^2 - x^3 - x^4