Sr Examen
Factorizar el polinomio 4*x^3-2*x+1
Solución
Factorización
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/ _______________ \ / _______________ \ / _______________\ | / ____ / ___\| | / ____ / ___\| | / ____ | | / 27 3*\/ 57 | 1 I*\/ 3 || | / 27 3*\/ 57 | 1 I*\/ 3 || | / 27 3*\/ 57 | | 3 / -- + -------- *|- - - -------|| | 3 / -- + -------- *|- - + -------|| | 3 / -- + -------- | | 1 \/ 8 8 \ 2 2 /| | 1 \/ 8 8 \ 2 2 /| | 1 \/ 8 8 | |x + -------------------------------------- + ------------------------------------|*|x + -------------------------------------- + ------------------------------------|*|x + ---------------------- + --------------------| | _______________ 3 | | _______________ 3 | | _______________ 3 | | / ___\ / ____ | | / ___\ / ____ | | / ____ | | | 1 I*\/ 3 | / 27 3*\/ 57 | | | 1 I*\/ 3 | / 27 3*\/ 57 | | / 27 3*\/ 57 | | 2*|- - - -------|*3 / -- + -------- | | 2*|- - + -------|*3 / -- + -------- | | 2*3 / -- + -------- | \ \ 2 2 / \/ 8 8 / \ \ 2 2 / \/ 8 8 / \ \/ 8 8 /
$$\left(x + \left(\frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{57}}{8} + \frac{27}{8}}}{3} + \frac{1}{2 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{57}}{8} + \frac{27}{8}}}\right)\right) \left(x + \left(\frac{1}{2 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{57}}{8} + \frac{27}{8}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3 \sqrt{57}}{8} + \frac{27}{8}}}{3}\right)\right) \left(x + \left(\frac{1}{2 \sqrt[3]{\frac{3 \sqrt{57}}{8} + \frac{27}{8}}} + \frac{\sqrt[3]{\frac{3 \sqrt{57}}{8} + \frac{27}{8}}}{3}\right)\right)$$
((x + 1/(2*(-1/2 - i*sqrt(3)/2)*(27/8 + 3*sqrt(57)/8)^(1/3)) + (27/8 + 3*sqrt(57)/8)^(1/3)*(-1/2 - i*sqrt(3)/2)/3)*(x + 1/(2*(-1/2 + i*sqrt(3)/2)*(27/8 + 3*sqrt(57)/8)^(1/3)) + (27/8 + 3*sqrt(57)/8)^(1/3)*(-1/2 + i*sqrt(3)/2)/3))*(x + 1/(2*(27/8 + 3*sqrt(57)/8)^(1/3)) + (27/8 + 3*sqrt(57)/8)^(1/3)/3)
Unión de expresiones racionales
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/ 2\ 1 + 2*x*\-1 + 2*x /
$$2 x \left(2 x^{2} - 1\right) + 1$$
1 + 2*x*(-1 + 2*x^2)