Sr Examen
Factorizar el polinomio x^4+5*x^3+2*x^2+5*x+1
Solución
Ha introducido
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4 3 2 x + 5*x + 2*x + 5*x + 1
$$\left(5 x + \left(2 x^{2} + \left(x^{4} + 5 x^{3}\right)\right)\right) + 1$$
x^4 + 5*x^3 + 2*x^2 + 5*x + 1
Simplificación general
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4 2 3 1 + x + 2*x + 5*x + 5*x
$$x^{4} + 5 x^{3} + 2 x^{2} + 5 x + 1$$
1 + x^4 + 2*x^2 + 5*x + 5*x^3
Factorización
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/ ____\ / ____\
| 5 \/ 21 | | 5 \/ 21 |
(x + I)*(x - I)*|x + - + ------|*|x + - - ------|
\ 2 2 / \ 2 2 /
$$\left(x - i\right) \left(x + i\right) \left(x + \left(\frac{\sqrt{21}}{2} + \frac{5}{2}\right)\right) \left(x + \left(\frac{5}{2} - \frac{\sqrt{21}}{2}\right)\right)$$
(((x + i)*(x - i))*(x + 5/2 + sqrt(21)/2))*(x + 5/2 - sqrt(21)/2)
Unión de expresiones racionales
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1 + x*(5 + x*(2 + x*(5 + x)))
$$x \left(x \left(x \left(x + 5\right) + 2\right) + 5\right) + 1$$
1 + x*(5 + x*(2 + x*(5 + x)))
Parte trigonométrica
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4 2 3 1 + x + 2*x + 5*x + 5*x
$$x^{4} + 5 x^{3} + 2 x^{2} + 5 x + 1$$
1 + x^4 + 2*x^2 + 5*x + 5*x^3
Compilar la expresión
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4 2 3 1 + x + 2*x + 5*x + 5*x
$$x^{4} + 5 x^{3} + 2 x^{2} + 5 x + 1$$
1 + x^4 + 2*x^2 + 5*x + 5*x^3
Potencias
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4 2 3 1 + x + 2*x + 5*x + 5*x
$$x^{4} + 5 x^{3} + 2 x^{2} + 5 x + 1$$
1 + x^4 + 2*x^2 + 5*x + 5*x^3
Denominador racional
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4 2 3 1 + x + 2*x + 5*x + 5*x
$$x^{4} + 5 x^{3} + 2 x^{2} + 5 x + 1$$
1 + x^4 + 2*x^2 + 5*x + 5*x^3
Combinatoria
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/ 2\ / 2 \ \1 + x /*\1 + x + 5*x/
$$\left(x^{2} + 1\right) \left(x^{2} + 5 x + 1\right)$$
(1 + x^2)*(1 + x^2 + 5*x)
Respuesta numérica
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1.0 + x^4 + 2.0*x^2 + 5.0*x + 5.0*x^3
1.0 + x^4 + 2.0*x^2 + 5.0*x + 5.0*x^3
Denominador común
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4 2 3 1 + x + 2*x + 5*x + 5*x
$$x^{4} + 5 x^{3} + 2 x^{2} + 5 x + 1$$
1 + x^4 + 2*x^2 + 5*x + 5*x^3