Sr Examen
Factorizar el polinomio x+3*x^2+x^3/3+5*x^4/4
Solución
Ha introducido
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3 4
2 x 5*x
x + 3*x + -- + ----
3 4
$$\frac{5 x^{4}}{4} + \left(\frac{x^{3}}{3} + \left(3 x^{2} + x\right)\right)$$
x + 3*x^2 + x^3/3 + (5*x^4)/4
Simplificación general
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/ 2 3 \
x*\12 + 4*x + 15*x + 36*x/
----------------------------
12
$$\frac{x \left(15 x^{3} + 4 x^{2} + 36 x + 12\right)}{12}$$
x*(12 + 4*x^2 + 15*x^3 + 36*x)/12
Descomposición de una fracción
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x + 3*x^2 + x^3/3 + 5*x^4/4
$$\frac{5 x^{4}}{4} + \frac{x^{3}}{3} + 3 x^{2} + x$$
3 4
2 x 5*x
x + 3*x + -- + ----
3 4
Factorización
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/ _____________________ \ / _____________________ \ / _____________________ \ | / _______ / ___\ | | / _______ / ___\ | | / _______ | | / 26794 2*\/ 66457 | 1 I*\/ 3 | | | / 26794 2*\/ 66457 | 1 I*\/ 3 | | | / 26794 2*\/ 66457 | | 3 / ----- + ----------- *|- - - -------| | | 3 / ----- + ----------- *|- - + -------| | | 3 / ----- + ----------- | | 4 \/ 3375 25 \ 2 2 / 1604 | | 4 \/ 3375 25 \ 2 2 / 1604 | | 4 \/ 3375 25 1604 | x*|x + -- + ------------------------------------------ - ----------------------------------------------|*|x + -- + ------------------------------------------ - ----------------------------------------------|*|x + -- + -------------------------- - ------------------------------| | 45 3 _____________________| | 45 3 _____________________| | 45 3 _____________________| | / ___\ / _______ | | / ___\ / _______ | | / _______ | | | 1 I*\/ 3 | / 26794 2*\/ 66457 | | | 1 I*\/ 3 | / 26794 2*\/ 66457 | | / 26794 2*\/ 66457 | | 675*|- - - -------|*3 / ----- + ----------- | | 675*|- - + -------|*3 / ----- + ----------- | | 675*3 / ----- + ----------- | \ \ 2 2 / \/ 3375 25 / \ \ 2 2 / \/ 3375 25 / \ \/ 3375 25 /
$$x \left(x + \left(\frac{4}{45} + \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{26794}{3375} + \frac{2 \sqrt{66457}}{25}}}{3} - \frac{1604}{675 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{26794}{3375} + \frac{2 \sqrt{66457}}{25}}}\right)\right) \left(x + \left(\frac{4}{45} - \frac{1604}{675 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{26794}{3375} + \frac{2 \sqrt{66457}}{25}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{26794}{3375} + \frac{2 \sqrt{66457}}{25}}}{3}\right)\right) \left(x + \left(- \frac{1604}{675 \sqrt[3]{\frac{26794}{3375} + \frac{2 \sqrt{66457}}{25}}} + \frac{4}{45} + \frac{\sqrt[3]{\frac{26794}{3375} + \frac{2 \sqrt{66457}}{25}}}{3}\right)\right)$$
((x*(x + 4/45 + (26794/3375 + 2*sqrt(66457)/25)^(1/3)*(-1/2 - i*sqrt(3)/2)/3 - 1604/(675*(-1/2 - i*sqrt(3)/2)*(26794/3375 + 2*sqrt(66457)/25)^(1/3))))*(x + 4/45 + (26794/3375 + 2*sqrt(66457)/25)^(1/3)*(-1/2 + i*sqrt(3)/2)/3 - 1604/(675*(-1/2 + i*sqrt(3)/2)*(26794/3375 + 2*sqrt(66457)/25)^(1/3))))*(x + 4/45 + (26794/3375 + 2*sqrt(66457)/25)^(1/3)/3 - 1604/(675*(26794/3375 + 2*sqrt(66457)/25)^(1/3)))
Compilar la expresión
[src]
3 4
2 x 5*x
x + 3*x + -- + ----
3 4
$$\frac{5 x^{4}}{4} + \frac{x^{3}}{3} + 3 x^{2} + x$$
x + 3*x^2 + x^3/3 + 5*x^4/4
Unión de expresiones racionales
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/ 2 3 \
x*\12 + 4*x + 15*x + 36*x/
----------------------------
12
$$\frac{x \left(15 x^{3} + 4 x^{2} + 36 x + 12\right)}{12}$$
x*(12 + 4*x^2 + 15*x^3 + 36*x)/12
Denominador racional
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3 4 2
4*x + 12*x + 15*x + 36*x
---------------------------
12
$$\frac{15 x^{4} + 4 x^{3} + 36 x^{2} + 12 x}{12}$$
(4*x^3 + 12*x + 15*x^4 + 36*x^2)/12
Potencias
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3 4
2 x 5*x
x + 3*x + -- + ----
3 4
$$\frac{5 x^{4}}{4} + \frac{x^{3}}{3} + 3 x^{2} + x$$
x + 3*x^2 + x^3/3 + 5*x^4/4
Respuesta numérica
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x + 3.0*x^2 + 1.25*x^4 + 0.333333333333333*x^3
x + 3.0*x^2 + 1.25*x^4 + 0.333333333333333*x^3
Combinatoria
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/ 2 3 \
x*\12 + 4*x + 15*x + 36*x/
----------------------------
12
$$\frac{x \left(15 x^{3} + 4 x^{2} + 36 x + 12\right)}{12}$$
x*(12 + 4*x^2 + 15*x^3 + 36*x)/12
Parte trigonométrica
[src]
3 4
2 x 5*x
x + 3*x + -- + ----
3 4
$$\frac{5 x^{4}}{4} + \frac{x^{3}}{3} + 3 x^{2} + x$$
x + 3*x^2 + x^3/3 + 5*x^4/4
Denominador común
[src]
3 4
2 x 5*x
x + 3*x + -- + ----
3 4
$$\frac{5 x^{4}}{4} + \frac{x^{3}}{3} + 3 x^{2} + x$$
x + 3*x^2 + x^3/3 + 5*x^4/4