Господин Экзамен
Разложить многочлен на множители 5*x^2-27*x+10*x^3-125
Решение
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2 3 5*x - 27*x + 10*x - 125
$$10 x^{3} + 5 x^{2} - 27 x - 125$$
5*x^2 - 27*x + 10*x^3 - 1*125
Разложение на множители
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/ ______________________ \ / ______________________ \ / ______________________ \ | / ___________ / ___\ | | / ___________ / ___\ | | / ___________ | | 1 / 3251 \/ 114845865 | 1 I*\/ 3 | 167 | | 1 / 3251 \/ 114845865 | 1 I*\/ 3 | 167 | | 1 / 3251 \/ 114845865 167 | 1*|x + - - 3 / ---- + ------------- *|- - - -------| - -----------------------------------------------|*|x + - - 3 / ---- + ------------- *|- - + -------| - -----------------------------------------------|*|x + - - 3 / ---- + ------------- - -------------------------------| | 6 \/ 540 1800 \ 2 2 / ______________________| | 6 \/ 540 1800 \ 2 2 / ______________________| | 6 \/ 540 1800 ______________________| | / ___\ / ___________ | | / ___\ / ___________ | | / ___________ | | | 1 I*\/ 3 | / 3251 \/ 114845865 | | | 1 I*\/ 3 | / 3251 \/ 114845865 | | / 3251 \/ 114845865 | | 180*|- - - -------|*3 / ---- + ------------- | | 180*|- - + -------|*3 / ---- + ------------- | | 180*3 / ---- + ------------- | \ \ 2 2 / \/ 540 1800 / \ \ 2 2 / \/ 540 1800 / \ \/ 540 1800 /
$$1 \left(x - \left(- \frac{1}{6} + \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{\sqrt{114845865}}{1800} + \frac{3251}{540}} + \frac{167}{180 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{\sqrt{114845865}}{1800} + \frac{3251}{540}}}\right)\right) \left(x - \left(- \frac{1}{6} + \frac{167}{180 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{\sqrt{114845865}}{1800} + \frac{3251}{540}}} + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{\sqrt{114845865}}{1800} + \frac{3251}{540}}\right)\right) \left(x - \left(- \frac{1}{6} + \frac{167}{180 \sqrt[3]{\frac{\sqrt{114845865}}{1800} + \frac{3251}{540}}} + \sqrt[3]{\frac{\sqrt{114845865}}{1800} + \frac{3251}{540}}\right)\right)$$
((1*(x + (1/6 - (3251/540 + sqrt(114845865)/1800)^(1/3)*(-1/2 - i*sqrt(3)/2) - 167/(180*(-1/2 - i*sqrt(3)/2)*(3251/540 + sqrt(114845865)/1800)^(1/3)))))*(x + (1/6 - (3251/540 + sqrt(114845865)/1800)^(1/3)*(-1/2 + i*sqrt(3)/2) - 167/(180*(-1/2 + i*sqrt(3)/2)*(3251/540 + sqrt(114845865)/1800)^(1/3)))))*(x + (1/6 - (3251/540 + sqrt(114845865)/1800)^(1/3) - 167/(180*(3251/540 + sqrt(114845865)/1800)^(1/3))))