Господин Экзамен
Разложить многочлен на множители 8*x^7-3*x^3+12*x*y^7-39
Решение
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7 3 7 8*x - 3*x + 12*x*y - 39
$$12 x y^{7} + 8 x^{7} - 3 x^{3} - 39$$
8*x^7 - 3*x^3 + 12*x*y^7 - 1*39
Разложение на множители
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/ ____________________\ / ____________________ ____________________ \ / ____________________ ____________________ \ / ____________________ ____________________ \ / ____________________ ____________________ \ / ____________________ ____________________ \ / ____________________ ____________________ \ | 7 _______ / 6 2 39 | | 7 _______ / 6 2 39 /pi\ 7 _______ / 6 2 39 /pi\| | 7 _______ / 6 2 39 /pi\ 7 _______ / 6 2 39 /pi\| | 7 _______ / 6 2 39 /2*pi\ 7 _______ / 6 2 39 /2*pi\| | 7 _______ / 6 2 39 /2*pi\ 7 _______ / 6 2 39 /2*pi\| | 7 _______ / 6 2 39 /3*pi\ 7 _______ / 6 2 39 /3*pi\| | 7 _______ / 6 2 39 /3*pi\ 7 _______ / 6 2 39 /3*pi\| | \/ 23328 *7 / - 8*x + 3*x + -- | | \/ 23328 *7 / - 8*x + 3*x + -- *cos|--| I*\/ 23328 *7 / - 8*x + 3*x + -- *sin|--|| | \/ 23328 *7 / - 8*x + 3*x + -- *cos|--| I*\/ 23328 *7 / - 8*x + 3*x + -- *sin|--|| | \/ 23328 *7 / - 8*x + 3*x + -- *cos|----| I*\/ 23328 *7 / - 8*x + 3*x + -- *sin|----|| | \/ 23328 *7 / - 8*x + 3*x + -- *cos|----| I*\/ 23328 *7 / - 8*x + 3*x + -- *sin|----|| | \/ 23328 *7 / - 8*x + 3*x + -- *cos|----| I*\/ 23328 *7 / - 8*x + 3*x + -- *sin|----|| | \/ 23328 *7 / - 8*x + 3*x + -- *cos|----| I*\/ 23328 *7 / - 8*x + 3*x + -- *sin|----|| | \/ x | | \/ x \7 / \/ x \7 /| | \/ x \7 / \/ x \7 /| | \/ x \ 7 / \/ x \ 7 /| | \/ x \ 7 / \/ x \ 7 /| | \/ x \ 7 / \/ x \ 7 /| | \/ x \ 7 / \/ x \ 7 /| 1*|y - ----------------------------------|*|y + ------------------------------------------ + --------------------------------------------|*|y + ------------------------------------------ - --------------------------------------------|*|y + - -------------------------------------------- + ----------------------------------------------|*|y + - -------------------------------------------- - ----------------------------------------------|*|y + -------------------------------------------- + ----------------------------------------------|*|y + -------------------------------------------- - ----------------------------------------------| \ 6 / \ 6 6 / \ 6 6 / \ 6 6 / \ 6 6 / \ 6 6 / \ 6 6 /
$$1 \left(y - \frac{\sqrt[7]{23328} \sqrt[7]{- 8 x^{6} + 3 x^{2} + \frac{39}{x}}}{6}\right) \left(y + \left(\frac{\sqrt[7]{23328} \sqrt[7]{- 8 x^{6} + 3 x^{2} + \frac{39}{x}} \cos{\left(\frac{\pi}{7} \right)}}{6} + \frac{\sqrt[7]{23328} i \sqrt[7]{- 8 x^{6} + 3 x^{2} + \frac{39}{x}} \sin{\left(\frac{\pi}{7} \right)}}{6}\right)\right) \left(y + \left(\frac{\sqrt[7]{23328} \sqrt[7]{- 8 x^{6} + 3 x^{2} + \frac{39}{x}} \cos{\left(\frac{\pi}{7} \right)}}{6} - \frac{\sqrt[7]{23328} i \sqrt[7]{- 8 x^{6} + 3 x^{2} + \frac{39}{x}} \sin{\left(\frac{\pi}{7} \right)}}{6}\right)\right) \left(y - \left(\frac{\sqrt[7]{23328} \sqrt[7]{- 8 x^{6} + 3 x^{2} + \frac{39}{x}} \cos{\left(\frac{2 \pi}{7} \right)}}{6} - \frac{\sqrt[7]{23328} i \sqrt[7]{- 8 x^{6} + 3 x^{2} + \frac{39}{x}} \sin{\left(\frac{2 \pi}{7} \right)}}{6}\right)\right) \left(y - \left(\frac{\sqrt[7]{23328} \sqrt[7]{- 8 x^{6} + 3 x^{2} + \frac{39}{x}} \cos{\left(\frac{2 \pi}{7} \right)}}{6} + \frac{\sqrt[7]{23328} i \sqrt[7]{- 8 x^{6} + 3 x^{2} + \frac{39}{x}} \sin{\left(\frac{2 \pi}{7} \right)}}{6}\right)\right) \left(y + \left(\frac{\sqrt[7]{23328} \sqrt[7]{- 8 x^{6} + 3 x^{2} + \frac{39}{x}} \cos{\left(\frac{3 \pi}{7} \right)}}{6} + \frac{\sqrt[7]{23328} i \sqrt[7]{- 8 x^{6} + 3 x^{2} + \frac{39}{x}} \sin{\left(\frac{3 \pi}{7} \right)}}{6}\right)\right) \left(y + \left(\frac{\sqrt[7]{23328} \sqrt[7]{- 8 x^{6} + 3 x^{2} + \frac{39}{x}} \cos{\left(\frac{3 \pi}{7} \right)}}{6} - \frac{\sqrt[7]{23328} i \sqrt[7]{- 8 x^{6} + 3 x^{2} + \frac{39}{x}} \sin{\left(\frac{3 \pi}{7} \right)}}{6}\right)\right)$$
((((((1*(y - 23328^(1/7)*(-8*x^6 + 3*x^2 + 39/x)^(1/7)/6))*(y + (23328^(1/7)*(-8*x^6 + 3*x^2 + 39/x)^(1/7)*cos(pi/7)/6 + i*23328^(1/7)*(-8*x^6 + 3*x^2 + 39/x)^(1/7)*sin(pi/7)/6)))*(y + (23328^(1/7)*(-8*x^6 + 3*x^2 + 39/x)^(1/7)*cos(pi/7)/6 - i*23328^(1/7)*(-8*x^6 + 3*x^2 + 39/x)^(1/7)*sin(pi/7)/6)))*(y - (23328^(1/7)*(-8*x^6 + 3*x^2 + 39/x)^(1/7)*cos(2*pi/7)/6 + i*23328^(1/7)*(-8*x^6 + 3*x^2 + 39/x)^(1/7)*sin(2*pi/7)/6)))*(y - (23328^(1/7)*(-8*x^6 + 3*x^2 + 39/x)^(1/7)*cos(2*pi/7)/6 - i*23328^(1/7)*(-8*x^6 + 3*x^2 + 39/x)^(1/7)*sin(2*pi/7)/6)))*(y + (23328^(1/7)*(-8*x^6 + 3*x^2 + 39/x)^(1/7)*cos(3*pi/7)/6 + i*23328^(1/7)*(-8*x^6 + 3*x^2 + 39/x)^(1/7)*sin(3*pi/7)/6)))*(y + (23328^(1/7)*(-8*x^6 + 3*x^2 + 39/x)^(1/7)*cos(3*pi/7)/6 - i*23328^(1/7)*(-8*x^6 + 3*x^2 + 39/x)^(1/7)*sin(3*pi/7)/6))