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