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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/ __________________ / ___\\ / __________________ / ___\\ | 3 / ______ | 1 I*\/ 3 || | 3 / ______ | 1 I*\/ 3 || / __________________\ | \/ 550 + 6*\/ 4497 *|- - - -------|| | \/ 550 + 6*\/ 4497 *|- - + -------|| | 3 / ______ | | 4 52 \ 2 2 /| | 4 52 \ 2 2 /| | 4 52 \/ 550 + 6*\/ 4497 | |x + - + --------------------------------------- + -------------------------------------|*|x + - + --------------------------------------- + -------------------------------------|*|x + - + ----------------------- + ---------------------| | 3 __________________ / ___\ 3 | | 3 __________________ / ___\ 3 | | 3 __________________ 3 | | 3 / ______ | 1 I*\/ 3 | | | 3 / ______ | 1 I*\/ 3 | | | 3 / ______ | | 3*\/ 550 + 6*\/ 4497 *|- - - -------| | | 3*\/ 550 + 6*\/ 4497 *|- - + -------| | \ 3*\/ 550 + 6*\/ 4497 / \ \ 2 2 / / \ \ 2 2 / /
$$\left(x + \left(\frac{4}{3} + \frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 \sqrt{4497} + 550}}{3} + \frac{52}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 \sqrt{4497} + 550}}\right)\right) \left(x + \left(\frac{4}{3} + \frac{52}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 \sqrt{4497} + 550}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{6 \sqrt{4497} + 550}}{3}\right)\right) \left(x + \left(\frac{4}{3} + \frac{52}{3 \sqrt[3]{6 \sqrt{4497} + 550}} + \frac{\sqrt[3]{6 \sqrt{4497} + 550}}{3}\right)\right)$$
((x + 4/3 + 52/(3*(550 + 6*sqrt(4497))^(1/3)*(-1/2 - i*sqrt(3)/2)) + (550 + 6*sqrt(4497))^(1/3)*(-1/2 - i*sqrt(3)/2)/3)*(x + 4/3 + 52/(3*(550 + 6*sqrt(4497))^(1/3)*(-1/2 + i*sqrt(3)/2)) + (550 + 6*sqrt(4497))^(1/3)*(-1/2 + i*sqrt(3)/2)/3))*(x + 4/3 + 52/(3*(550 + 6*sqrt(4497))^(1/3)) + (550 + 6*sqrt(4497))^(1/3)/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
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
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
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))