Sr Examen
Factorizar el polinomio x^4+9*x-2*x^3/3
Solución
Ha introducido
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3
4 2*x
x + 9*x - ----
3
$$- \frac{2 x^{3}}{3} + \left(x^{4} + 9 x\right)$$
x^4 + 9*x - 2*x^3/3
Descomposición de una fracción
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x^4 + 9*x - 2*x^3/3
$$x^{4} - \frac{2 x^{3}}{3} + 9 x$$
3
4 2*x
x + 9*x - ----
3
Factorización
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/ ___________________ \ / ___________________ \ / ___________________\ | / ______ / ___\| | / ______ / ___\| | / ______ | | / 6545 3*\/ 6529 | 1 I*\/ 3 || | / 6545 3*\/ 6529 | 1 I*\/ 3 || | / 6545 3*\/ 6529 | | 3 / ---- + ---------- *|- - - -------|| | 3 / ---- + ---------- *|- - + -------|| | 3 / ---- + ---------- | | 2 4 \/ 54 2 \ 2 2 /| | 2 4 \/ 54 2 \ 2 2 /| | 2 4 \/ 54 2 | x*|x + - - + ------------------------------------------- + ----------------------------------------|*|x + - - + ------------------------------------------- + ----------------------------------------|*|x + - - + --------------------------- + ------------------------| | 9 ___________________ 3 | | 9 ___________________ 3 | | 9 ___________________ 3 | | / ___\ / ______ | | / ___\ / ______ | | / ______ | | | 1 I*\/ 3 | / 6545 3*\/ 6529 | | | 1 I*\/ 3 | / 6545 3*\/ 6529 | | / 6545 3*\/ 6529 | | 27*|- - - -------|*3 / ---- + ---------- | | 27*|- - + -------|*3 / ---- + ---------- | | 27*3 / ---- + ---------- | \ \ 2 2 / \/ 54 2 / \ \ 2 2 / \/ 54 2 / \ \/ 54 2 /
$$x \left(x + \left(- \frac{2}{9} + \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{6529}}{2} + \frac{6545}{54}}}{3} + \frac{4}{27 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{6529}}{2} + \frac{6545}{54}}}\right)\right) \left(x + \left(- \frac{2}{9} + \frac{4}{27 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{6529}}{2} + \frac{6545}{54}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{6529}}{2} + \frac{6545}{54}}}{3}\right)\right) \left(x + \left(- \frac{2}{9} + \frac{4}{27 \sqrt[3]{\frac{3 \sqrt{6529}}{2} + \frac{6545}{54}}} + \frac{\sqrt[3]{\frac{3 \sqrt{6529}}{2} + \frac{6545}{54}}}{3}\right)\right)$$
((x*(x - 2/9 + 4/(27*(-1/2 - i*sqrt(3)/2)*(6545/54 + 3*sqrt(6529)/2)^(1/3)) + (6545/54 + 3*sqrt(6529)/2)^(1/3)*(-1/2 - i*sqrt(3)/2)/3))*(x - 2/9 + 4/(27*(-1/2 + i*sqrt(3)/2)*(6545/54 + 3*sqrt(6529)/2)^(1/3)) + (6545/54 + 3*sqrt(6529)/2)^(1/3)*(-1/2 + i*sqrt(3)/2)/3))*(x - 2/9 + 4/(27*(6545/54 + 3*sqrt(6529)/2)^(1/3)) + (6545/54 + 3*sqrt(6529)/2)^(1/3)/3)
Simplificación general
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/ 2\ | 3 2*x | x*|9 + x - ----| \ 3 /
$$x \left(x^{3} - \frac{2 x^{2}}{3} + 9\right)$$
x*(9 + x^3 - 2*x^2/3)
Denominador racional
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3 4
- 2*x + 3*x + 27*x
--------------------
3
$$\frac{3 x^{4} - 2 x^{3} + 27 x}{3}$$
(-2*x^3 + 3*x^4 + 27*x)/3
Compilar la expresión
[src]
3
4 2*x
x + 9*x - ----
3
$$x^{4} - \frac{2 x^{3}}{3} + 9 x$$
x^4 + 9*x - 2*x^3/3
Unión de expresiones racionales
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/ 2 3\
x*\27 - 2*x + 3*x /
--------------------
3
$$\frac{x \left(3 x^{3} - 2 x^{2} + 27\right)}{3}$$
x*(27 - 2*x^2 + 3*x^3)/3
Parte trigonométrica
[src]
3
4 2*x
x + 9*x - ----
3
$$x^{4} - \frac{2 x^{3}}{3} + 9 x$$
x^4 + 9*x - 2*x^3/3
Combinatoria
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/ 2 3\
x*\27 - 2*x + 3*x /
--------------------
3
$$\frac{x \left(3 x^{3} - 2 x^{2} + 27\right)}{3}$$
x*(27 - 2*x^2 + 3*x^3)/3
Denominador común
[src]
3
4 2*x
x + 9*x - ----
3
$$x^{4} - \frac{2 x^{3}}{3} + 9 x$$
x^4 + 9*x - 2*x^3/3