Sr Examen
Factorizar el polinomio x^3+3*x^2*y-6*x*y^2-2^3
Solución
Ha introducido
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3 2 2 x + 3*x *y - 6*x*y - 8
$$\left(- 6 x y^{2} + \left(x^{3} + 3 x^{2} y\right)\right) - 8$$
x^3 + (3*x^2)*y - 6*x*y^2 - 8
Simplificación general
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3 2 2 -8 + x - 6*x*y + 3*y*x
$$x^{3} + 3 x^{2} y - 6 x y^{2} - 8$$
-8 + x^3 - 6*x*y^2 + 3*y*x^2
Factorización
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$$\left(x + \left(\frac{9 y^{2}}{\sqrt[3]{108 y^{3} + \frac{\sqrt{- 78732 y^{6} + \left(216 y^{3} - 216\right)^{2}}}{2} - 108}} + y + \frac{\sqrt[3]{108 y^{3} + \frac{\sqrt{- 78732 y^{6} + \left(216 y^{3} - 216\right)^{2}}}{2} - 108}}{3}\right)\right) \left(x + \left(\frac{9 y^{2}}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{108 y^{3} + \frac{\sqrt{- 78732 y^{6} + \left(216 y^{3} - 216\right)^{2}}}{2} - 108}} + y + \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{108 y^{3} + \frac{\sqrt{- 78732 y^{6} + \left(216 y^{3} - 216\right)^{2}}}{2} - 108}}{3}\right)\right) \left(x + \left(\frac{9 y^{2}}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{108 y^{3} + \frac{\sqrt{- 78732 y^{6} + \left(216 y^{3} - 216\right)^{2}}}{2} - 108}} + y + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{108 y^{3} + \frac{\sqrt{- 78732 y^{6} + \left(216 y^{3} - 216\right)^{2}}}{2} - 108}}{3}\right)\right)$$
((x + y + (-108 + sqrt((-216 + 216*y^3)^2 - 78732*y^6)/2 + 108*y^3)^(1/3)/3 + 9*y^2/(-108 + sqrt((-216 + 216*y^3)^2 - 78732*y^6)/2 + 108*y^3)^(1/3))*(x + y + (-108 + sqrt((-216 + 216*y^3)^2 - 78732*y^6)/2 + 108*y^3)^(1/3)*(-1/2 - i*sqrt(3)/2)/3 + 9*y^2/((-1/2 - i*sqrt(3)/2)*(-108 + sqrt((-216 + 216*y^3)^2 - 78732*y^6)/2 + 108*y^3)^(1/3))))*(x + y + (-108 + sqrt((-216 + 216*y^3)^2 - 78732*y^6)/2 + 108*y^3)^(1/3)*(-1/2 + i*sqrt(3)/2)/3 + 9*y^2/((-1/2 + i*sqrt(3)/2)*(-108 + sqrt((-216 + 216*y^3)^2 - 78732*y^6)/2 + 108*y^3)^(1/3)))
Compilar la expresión
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3 2 2 -8 + x - 6*x*y + 3*y*x
$$x^{3} + 3 x^{2} y - 6 x y^{2} - 8$$
-8 + x^3 - 6*x*y^2 + 3*y*x^2
Combinatoria
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3 2 2 -8 + x - 6*x*y + 3*y*x
$$x^{3} + 3 x^{2} y - 6 x y^{2} - 8$$
-8 + x^3 - 6*x*y^2 + 3*y*x^2
Denominador común
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3 2 2 -8 + x - 6*x*y + 3*y*x
$$x^{3} + 3 x^{2} y - 6 x y^{2} - 8$$
-8 + x^3 - 6*x*y^2 + 3*y*x^2
Parte trigonométrica
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3 2 2 -8 + x - 6*x*y + 3*y*x
$$x^{3} + 3 x^{2} y - 6 x y^{2} - 8$$
-8 + x^3 - 6*x*y^2 + 3*y*x^2
Unión de expresiones racionales
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/ 2 \ -8 + x*\- 6*y + x*(x + 3*y)/
$$x \left(x \left(x + 3 y\right) - 6 y^{2}\right) - 8$$
-8 + x*(-6*y^2 + x*(x + 3*y))
Denominador racional
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3 2 2 -8 + x - 6*x*y + 3*y*x
$$x^{3} + 3 x^{2} y - 6 x y^{2} - 8$$
-8 + x^3 - 6*x*y^2 + 3*y*x^2
Potencias
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3 2 2 -8 + x - 6*x*y + 3*y*x
$$x^{3} + 3 x^{2} y - 6 x y^{2} - 8$$
-8 + x^3 - 6*x*y^2 + 3*y*x^2