Sr Examen
Factorizar el polinomio x^6/6+3*x^4/8+7*x^3/3
Solución
Ha introducido
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6 4 3 x 3*x 7*x -- + ---- + ---- 6 8 3
$$\frac{7 x^{3}}{3} + \left(\frac{x^{6}}{6} + \frac{3 x^{4}}{8}\right)$$
x^6/6 + (3*x^4)/8 + (7*x^3)/3
Descomposición de una fracción
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x^6/6 + 3*x^4/8 + 7*x^3/3
$$\frac{x^{6}}{6} + \frac{3 x^{4}}{8} + \frac{7 x^{3}}{3}$$
6 4 3 x 3*x 7*x -- + ---- + ---- 6 8 3
Factorización
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/ ___________________ \ / ___________________ \ / ___________________ \ | / ______ / ___\ | | / ______ / ___\ | | / ______ | | / 27*\/ 3163 | 1 I*\/ 3 | | | / 27*\/ 3163 | 1 I*\/ 3 | | | / 27*\/ 3163 | | 3 / 189 + ----------- *|- - - -------| | | 3 / 189 + ----------- *|- - + -------| | | 3 / 189 + ----------- | | \/ 8 \ 2 2 / 9 | | \/ 8 \ 2 2 / 9 | | \/ 8 9 | x*|x + ---------------------------------------- - ------------------------------------------|*|x + ---------------------------------------- - ------------------------------------------|*|x + ------------------------ - --------------------------| | 3 ___________________ | | 3 ___________________ | | 3 ___________________| | / ______ / ___\| | / ______ / ___\| | / ______ | | / 27*\/ 3163 | 1 I*\/ 3 || | / 27*\/ 3163 | 1 I*\/ 3 || | / 27*\/ 3163 | | 4*3 / 189 + ----------- *|- - - -------|| | 4*3 / 189 + ----------- *|- - + -------|| | 4*3 / 189 + ----------- | \ \/ 8 \ 2 2 // \ \/ 8 \ 2 2 // \ \/ 8 /
$$x \left(x + \left(\frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{189 + \frac{27 \sqrt{3163}}{8}}}{3} - \frac{9}{4 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{189 + \frac{27 \sqrt{3163}}{8}}}\right)\right) \left(x + \left(- \frac{9}{4 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{189 + \frac{27 \sqrt{3163}}{8}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{189 + \frac{27 \sqrt{3163}}{8}}}{3}\right)\right) \left(x + \left(- \frac{9}{4 \sqrt[3]{189 + \frac{27 \sqrt{3163}}{8}}} + \frac{\sqrt[3]{189 + \frac{27 \sqrt{3163}}{8}}}{3}\right)\right)$$
((x*(x + (189 + 27*sqrt(3163)/8)^(1/3)*(-1/2 - i*sqrt(3)/2)/3 - 9/(4*(189 + 27*sqrt(3163)/8)^(1/3)*(-1/2 - i*sqrt(3)/2))))*(x + (189 + 27*sqrt(3163)/8)^(1/3)*(-1/2 + i*sqrt(3)/2)/3 - 9/(4*(189 + 27*sqrt(3163)/8)^(1/3)*(-1/2 + i*sqrt(3)/2))))*(x + (189 + 27*sqrt(3163)/8)^(1/3)/3 - 9/(4*(189 + 27*sqrt(3163)/8)^(1/3)))
Simplificación general
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3 / 3 \
x *\56 + 4*x + 9*x/
--------------------
24
$$\frac{x^{3} \left(4 x^{3} + 9 x + 56\right)}{24}$$
x^3*(56 + 4*x^3 + 9*x)/24
Respuesta numérica
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0.375*x^4 + 2.33333333333333*x^3 + 0.166666666666667*x^6
0.375*x^4 + 2.33333333333333*x^3 + 0.166666666666667*x^6
Compilar la expresión
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6 4 3 x 3*x 7*x -- + ---- + ---- 6 8 3
$$\frac{x^{6}}{6} + \frac{3 x^{4}}{8} + \frac{7 x^{3}}{3}$$
x^6/6 + 3*x^4/8 + 7*x^3/3
Denominador racional
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6 4 3
24*x + 54*x + 336*x
----------------------
144
$$\frac{24 x^{6} + 54 x^{4} + 336 x^{3}}{144}$$
(24*x^6 + 54*x^4 + 336*x^3)/144
Denominador común
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6 4 3 x 3*x 7*x -- + ---- + ---- 6 8 3
$$\frac{x^{6}}{6} + \frac{3 x^{4}}{8} + \frac{7 x^{3}}{3}$$
x^6/6 + 3*x^4/8 + 7*x^3/3
Potencias
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6 4 3 x 3*x 7*x -- + ---- + ---- 6 8 3
$$\frac{x^{6}}{6} + \frac{3 x^{4}}{8} + \frac{7 x^{3}}{3}$$
x^6/6 + 3*x^4/8 + 7*x^3/3
Unión de expresiones racionales
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3 / / 2\\
x *\56 + x*\9 + 4*x //
----------------------
24
$$\frac{x^{3} \left(x \left(4 x^{2} + 9\right) + 56\right)}{24}$$
x^3*(56 + x*(9 + 4*x^2))/24
Combinatoria
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3 / 3 \
x *\56 + 4*x + 9*x/
--------------------
24
$$\frac{x^{3} \left(4 x^{3} + 9 x + 56\right)}{24}$$
x^3*(56 + 4*x^3 + 9*x)/24
Parte trigonométrica
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6 4 3 x 3*x 7*x -- + ---- + ---- 6 8 3
$$\frac{x^{6}}{6} + \frac{3 x^{4}}{8} + \frac{7 x^{3}}{3}$$
x^6/6 + 3*x^4/8 + 7*x^3/3