Sr Examen
Factorizar el polinomio x^6-x^5+x^4-x^3+x^2-x+1
Solución
Ha introducido
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6 5 4 3 2 x - x + x - x + x - x + 1
$$\left(- x + \left(x^{2} + \left(- x^{3} + \left(x^{4} + \left(x^{6} - x^{5}\right)\right)\right)\right)\right) + 1$$
x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Simplificación general
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2 4 6 3 5 1 + x + x + x - x - x - x
$$x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$$
1 + x^2 + x^4 + x^6 - x - x^3 - x^5
Factorización
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/ /pi\ /pi\\ / /pi\ /pi\\ / /2*pi\ /2*pi\\ / /2*pi\ /2*pi\\ / /3*pi\ /3*pi\\ / /3*pi\ /3*pi\\ |x + I*sin|--| - cos|--||*|x + - I*sin|--| - cos|--||*|x + cos|----| + I*sin|----||*|x + cos|----| - I*sin|----||*|x + I*sin|----| - cos|----||*|x + - I*sin|----| - cos|----|| \ \7 / \7 // \ \7 / \7 // \ \ 7 / \ 7 // \ \ 7 / \ 7 // \ \ 7 / \ 7 // \ \ 7 / \ 7 //
$$\left(x + \left(- \cos{\left(\frac{\pi}{7} \right)} - i \sin{\left(\frac{\pi}{7} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{\pi}{7} \right)} + i \sin{\left(\frac{\pi}{7} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{2 \pi}{7} \right)} + i \sin{\left(\frac{2 \pi}{7} \right)}\right)\right) \left(x + \left(\cos{\left(\frac{2 \pi}{7} \right)} - i \sin{\left(\frac{2 \pi}{7} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{3 \pi}{7} \right)} + i \sin{\left(\frac{3 \pi}{7} \right)}\right)\right) \left(x + \left(- \cos{\left(\frac{3 \pi}{7} \right)} - i \sin{\left(\frac{3 \pi}{7} \right)}\right)\right)$$
(((((x + i*sin(pi/7) - cos(pi/7))*(x - i*sin(pi/7) - cos(pi/7)))*(x + cos(2*pi/7) + i*sin(2*pi/7)))*(x + cos(2*pi/7) - i*sin(2*pi/7)))*(x + i*sin(3*pi/7) - cos(3*pi/7)))*(x - i*sin(3*pi/7) - cos(3*pi/7))
Respuesta numérica
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1.0 + x^2 + x^4 + x^6 - x - x^3 - x^5
1.0 + x^2 + x^4 + x^6 - x - x^3 - x^5
Potencias
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2 4 6 3 5 1 + x + x + x - x - x - x
$$x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$$
1 + x^2 + x^4 + x^6 - x - x^3 - x^5
Denominador racional
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2 4 6 3 5 1 + x + x + x - x - x - x
$$x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$$
1 + x^2 + x^4 + x^6 - x - x^3 - x^5
Compilar la expresión
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2 4 6 3 5 1 + x + x + x - x - x - x
$$x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$$
1 + x^2 + x^4 + x^6 - x - x^3 - x^5
Parte trigonométrica
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2 4 6 3 5 1 + x + x + x - x - x - x
$$x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$$
1 + x^2 + x^4 + x^6 - x - x^3 - x^5
Unión de expresiones racionales
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1 + x*(-1 + x*(1 + x*(-1 + x*(1 + x*(-1 + x)))))
$$x \left(x \left(x \left(x \left(x \left(x - 1\right) + 1\right) - 1\right) + 1\right) - 1\right) + 1$$
1 + x*(-1 + x*(1 + x*(-1 + x*(1 + x*(-1 + x)))))
Denominador común
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2 4 6 3 5 1 + x + x + x - x - x - x
$$x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$$
1 + x^2 + x^4 + x^6 - x - x^3 - x^5
Combinatoria
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2 4 6 3 5 1 + x + x + x - x - x - x
$$x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$$
1 + x^2 + x^4 + x^6 - x - x^3 - x^5