Sr Examen
Factorizar el polinomio x+3*x^2+x^4/4
Solución
Ha introducido
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4
2 x
x + 3*x + --
4
$$\frac{x^{4}}{4} + \left(3 x^{2} + x\right)$$
x + 3*x^2 + x^4/4
Descomposición de una fracción
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x + 3*x^2 + x^4/4
$$\frac{x^{4}}{4} + 3 x^{2} + x$$
4
2 x
x + 3*x + --
4
Factorización
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/ ________________ / ___\\ / ________________ / ___\\ | 3 / ____ | 1 I*\/ 3 || | 3 / ____ | 1 I*\/ 3 || / ________________\ | \/ 54 + 54*\/ 17 *|- - - -------|| | \/ 54 + 54*\/ 17 *|- - + -------|| | 3 / ____ | | 12 \ 2 2 /| | 12 \ 2 2 /| | 12 \/ 54 + 54*\/ 17 | x*|x + - ----------------------------------- + -----------------------------------|*|x + - ----------------------------------- + -----------------------------------|*|x + - ------------------- + -------------------| | ________________ / ___\ 3 | | ________________ / ___\ 3 | | ________________ 3 | | 3 / ____ | 1 I*\/ 3 | | | 3 / ____ | 1 I*\/ 3 | | | 3 / ____ | | \/ 54 + 54*\/ 17 *|- - - -------| | | \/ 54 + 54*\/ 17 *|- - + -------| | \ \/ 54 + 54*\/ 17 / \ \ 2 2 / / \ \ 2 2 / /
$$x \left(x + \left(\frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{54 + 54 \sqrt{17}}}{3} - \frac{12}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{54 + 54 \sqrt{17}}}\right)\right) \left(x + \left(- \frac{12}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{54 + 54 \sqrt{17}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{54 + 54 \sqrt{17}}}{3}\right)\right) \left(x + \left(- \frac{12}{\sqrt[3]{54 + 54 \sqrt{17}}} + \frac{\sqrt[3]{54 + 54 \sqrt{17}}}{3}\right)\right)$$
((x*(x - 12/((54 + 54*sqrt(17))^(1/3)*(-1/2 - i*sqrt(3)/2)) + (54 + 54*sqrt(17))^(1/3)*(-1/2 - i*sqrt(3)/2)/3))*(x - 12/((54 + 54*sqrt(17))^(1/3)*(-1/2 + i*sqrt(3)/2)) + (54 + 54*sqrt(17))^(1/3)*(-1/2 + i*sqrt(3)/2)/3))*(x - 12/(54 + 54*sqrt(17))^(1/3) + (54 + 54*sqrt(17))^(1/3)/3)
Simplificación general
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/ 3 \
x*\4 + x + 12*x/
-----------------
4
$$\frac{x \left(x^{3} + 12 x + 4\right)}{4}$$
x*(4 + x^3 + 12*x)/4
Denominador racional
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4 2
x + 4*x + 12*x
----------------
4
$$\frac{x^{4} + 12 x^{2} + 4 x}{4}$$
(x^4 + 4*x + 12*x^2)/4
Combinatoria
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/ 3 \
x*\4 + x + 12*x/
-----------------
4
$$\frac{x \left(x^{3} + 12 x + 4\right)}{4}$$
x*(4 + x^3 + 12*x)/4
Compilar la expresión
[src]
4
2 x
x + 3*x + --
4
$$\frac{x^{4}}{4} + 3 x^{2} + x$$
x + 3*x^2 + x^4/4
Unión de expresiones racionales
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/ 3 \
x*\4 + x + 12*x/
-----------------
4
$$\frac{x \left(x^{3} + 12 x + 4\right)}{4}$$
x*(4 + x^3 + 12*x)/4