Господин Экзамен
Разложить многочлен на множители x^3+4*x^2+x-4
Решение
Разложение на множители
[src]
/ ________________ \ / ________________ \ / ________________ \ | / _____ / ___\ | | / _____ / ___\ | | / _____ | | 4 / 8 I*\/ 237 | 1 I*\/ 3 | 13 | | 4 / 8 I*\/ 237 | 1 I*\/ 3 | 13 | | 4 / 8 I*\/ 237 13 | 1*|x + - - 3 / -- + --------- *|- - - -------| - ---------------------------------------|*|x + - - 3 / -- + --------- *|- - + -------| - ---------------------------------------|*|x + - - 3 / -- + --------- - -----------------------| | 3 \/ 27 9 \ 2 2 / ________________| | 3 \/ 27 9 \ 2 2 / ________________| | 3 \/ 27 9 ________________| | / ___\ / _____ | | / ___\ / _____ | | / _____ | | | 1 I*\/ 3 | / 8 I*\/ 237 | | | 1 I*\/ 3 | / 8 I*\/ 237 | | / 8 I*\/ 237 | | 9*|- - - -------|*3 / -- + --------- | | 9*|- - + -------|*3 / -- + --------- | | 9*3 / -- + --------- | \ \ 2 2 / \/ 27 9 / \ \ 2 2 / \/ 27 9 / \ \/ 27 9 /
$$1 \left(x - \left(- \frac{4}{3} + \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{8}{27} + \frac{\sqrt{237} i}{9}} + \frac{13}{9 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{8}{27} + \frac{\sqrt{237} i}{9}}}\right)\right) \left(x - \left(- \frac{4}{3} + \frac{13}{9 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{8}{27} + \frac{\sqrt{237} i}{9}}} + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{8}{27} + \frac{\sqrt{237} i}{9}}\right)\right) \left(x - \left(- \frac{4}{3} + \frac{13}{9 \sqrt[3]{\frac{8}{27} + \frac{\sqrt{237} i}{9}}} + \sqrt[3]{\frac{8}{27} + \frac{\sqrt{237} i}{9}}\right)\right)$$
((1*(x + (4/3 - (8/27 + i*sqrt(237)/9)^(1/3)*(-1/2 - i*sqrt(3)/2) - 13/(9*(-1/2 - i*sqrt(3)/2)*(8/27 + i*sqrt(237)/9)^(1/3)))))*(x + (4/3 - (8/27 + i*sqrt(237)/9)^(1/3)*(-1/2 + i*sqrt(3)/2) - 13/(9*(-1/2 + i*sqrt(3)/2)*(8/27 + i*sqrt(237)/9)^(1/3)))))*(x + (4/3 - (8/27 + i*sqrt(237)/9)^(1/3) - 13/(9*(8/27 + i*sqrt(237)/9)^(1/3))))