Господин Экзамен
Разложить многочлен на множители 125*c^3-753*c^2+15*c-1
Решение
Вы ввели
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3 2 125*c - 753*c + 15*c - 1
$$125 c^{3} - 753 c^{2} + 15 c - 1$$
125*c^3 - 753*c^2 + 15*c - 1*1
Разложение на множители
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/ _________________________ \ / _________________________ \ / _________________________ \ | / ______ / ___\ | | / ______ / ___\ | | / ______ | | 251 / 15585751 113*\/ 1129 | 1 I*\/ 3 | 62376 | | 251 / 15585751 113*\/ 1129 | 1 I*\/ 3 | 62376 | | 251 / 15585751 113*\/ 1129 62376 | 1*|c + - --- - 3 / -------- + ------------ *|- - - -------| - ----------------------------------------------------|*|c + - --- - 3 / -------- + ------------ *|- - + -------| - ----------------------------------------------------|*|c + - --- - 3 / -------- + ------------ - ------------------------------------| | 125 \/ 1953125 15625 \ 2 2 / _________________________| | 125 \/ 1953125 15625 \ 2 2 / _________________________| | 125 \/ 1953125 15625 _________________________| | / ___\ / ______ | | / ___\ / ______ | | / ______ | | | 1 I*\/ 3 | / 15585751 113*\/ 1129 | | | 1 I*\/ 3 | / 15585751 113*\/ 1129 | | / 15585751 113*\/ 1129 | | 15625*|- - - -------|*3 / -------- + ------------ | | 15625*|- - + -------|*3 / -------- + ------------ | | 15625*3 / -------- + ------------ | \ \ 2 2 / \/ 1953125 15625 / \ \ 2 2 / \/ 1953125 15625 / \ \/ 1953125 15625 /
$$1 \left(c - \left(\frac{251}{125} + \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{113 \sqrt{1129}}{15625} + \frac{15585751}{1953125}} + \frac{62376}{15625 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{113 \sqrt{1129}}{15625} + \frac{15585751}{1953125}}}\right)\right) \left(c - \left(\frac{251}{125} + \frac{62376}{15625 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{113 \sqrt{1129}}{15625} + \frac{15585751}{1953125}}} + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{113 \sqrt{1129}}{15625} + \frac{15585751}{1953125}}\right)\right) \left(c - \left(\frac{62376}{15625 \sqrt[3]{\frac{113 \sqrt{1129}}{15625} + \frac{15585751}{1953125}}} + \frac{251}{125} + \sqrt[3]{\frac{113 \sqrt{1129}}{15625} + \frac{15585751}{1953125}}\right)\right)$$
((1*(c - (251/125 - (15585751/1953125 + 113*sqrt(1129)/15625)^(1/3)*(-1/2 - i*sqrt(3)/2) - 62376/(15625*(-1/2 - i*sqrt(3)/2)*(15585751/1953125 + 113*sqrt(1129)/15625)^(1/3)))))*(c - (251/125 - (15585751/1953125 + 113*sqrt(1129)/15625)^(1/3)*(-1/2 + i*sqrt(3)/2) - 62376/(15625*(-1/2 + i*sqrt(3)/2)*(15585751/1953125 + 113*sqrt(1129)/15625)^(1/3)))))*(c - (251/125 - (15585751/1953125 + 113*sqrt(1129)/15625)^(1/3) - 62376/(15625*(15585751/1953125 + 113*sqrt(1129)/15625)^(1/3))))