Sr Examen
Factorizar el polinomio x^3-4*x^2-12*x+20
Solución
Ha introducido
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3 2 x - 4*x - 12*x + 20
$$\left(- 12 x + \left(x^{3} - 4 x^{2}\right)\right) + 20$$
x^3 - 4*x^2 - 12*x + 20
Factorización
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$$\left(x + \left(- \frac{4}{3} - \frac{52}{9 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10}{27} + \frac{2 \sqrt{3903} i}{9}}} - \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10}{27} + \frac{2 \sqrt{3903} i}{9}}\right)\right) \left(x + \left(- \frac{4}{3} - \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10}{27} + \frac{2 \sqrt{3903} i}{9}} - \frac{52}{9 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10}{27} + \frac{2 \sqrt{3903} i}{9}}}\right)\right) \left(x + \left(- \frac{4}{3} - \sqrt[3]{\frac{10}{27} + \frac{2 \sqrt{3903} i}{9}} - \frac{52}{9 \sqrt[3]{\frac{10}{27} + \frac{2 \sqrt{3903} i}{9}}}\right)\right)$$
((x - 4/3 - (10/27 + 2*i*sqrt(3903)/9)^(1/3)*(-1/2 - i*sqrt(3)/2) - 52/(9*(-1/2 - i*sqrt(3)/2)*(10/27 + 2*i*sqrt(3903)/9)^(1/3)))*(x - 4/3 - (10/27 + 2*i*sqrt(3903)/9)^(1/3)*(-1/2 + i*sqrt(3)/2) - 52/(9*(-1/2 + i*sqrt(3)/2)*(10/27 + 2*i*sqrt(3903)/9)^(1/3))))*(x - 4/3 - (10/27 + 2*i*sqrt(3903)/9)^(1/3) - 52/(9*(10/27 + 2*i*sqrt(3903)/9)^(1/3)))
Simplificación general
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3 2 20 + x - 12*x - 4*x
$$x^{3} - 4 x^{2} - 12 x + 20$$
20 + x^3 - 12*x - 4*x^2
Unión de expresiones racionales
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20 + x*(-12 + x*(-4 + x))
$$x \left(x \left(x - 4\right) - 12\right) + 20$$
20 + x*(-12 + x*(-4 + x))
Parte trigonométrica
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3 2 20 + x - 12*x - 4*x
$$x^{3} - 4 x^{2} - 12 x + 20$$
20 + x^3 - 12*x - 4*x^2
Denominador común
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3 2 20 + x - 12*x - 4*x
$$x^{3} - 4 x^{2} - 12 x + 20$$
20 + x^3 - 12*x - 4*x^2
Denominador racional
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3 2 20 + x - 12*x - 4*x
$$x^{3} - 4 x^{2} - 12 x + 20$$
20 + x^3 - 12*x - 4*x^2
Compilar la expresión
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3 2 20 + x - 12*x - 4*x
$$x^{3} - 4 x^{2} - 12 x + 20$$
20 + x^3 - 12*x - 4*x^2