Господин Экзамен
Раскрыть скобки в (x^3-5*x^2-4)*(x-3)
Решение
Вы ввели
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/ 3 2 \ \x - 5*x - 4/*(x - 3)
$$\left(x - 3\right) \left(x^{3} - 5 x^{2} - 4\right)$$
(x^3 - 5*x^2 - 1*4)*(x - 1*3)
Общее упрощение
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/ 3 2\ -(-3 + x)*\4 - x + 5*x /
$$- \left(x - 3\right) \left(- x^{3} + 5 x^{2} + 4\right)$$
-(-3 + x)*(4 - x^3 + 5*x^2)
Разложение на множители
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/ _________________ \ / _________________ \ / _________________ \
| / _____ / ___\ | | / _____ / ___\ | | / _____ |
| 5 / 179 4*\/ 114 | 1 I*\/ 3 | 25 | | 5 / 179 4*\/ 114 | 1 I*\/ 3 | 25 | | 5 / 179 4*\/ 114 25 |
1*(x - 3)*|x + - - - 3 / --- + --------- *|- - - -------| - ----------------------------------------|*|x + - - - 3 / --- + --------- *|- - + -------| - ----------------------------------------|*|x + - - - 3 / --- + --------- - ------------------------|
| 3 \/ 27 9 \ 2 2 / _________________| | 3 \/ 27 9 \ 2 2 / _________________| | 3 \/ 27 9 _________________|
| / ___\ / _____ | | / ___\ / _____ | | / _____ |
| | 1 I*\/ 3 | / 179 4*\/ 114 | | | 1 I*\/ 3 | / 179 4*\/ 114 | | / 179 4*\/ 114 |
| 9*|- - - -------|*3 / --- + --------- | | 9*|- - + -------|*3 / --- + --------- | | 9*3 / --- + --------- |
\ \ 2 2 / \/ 27 9 / \ \ 2 2 / \/ 27 9 / \ \/ 27 9 /
$$1 \left(x - 3\right) \left(x - \left(\frac{5}{3} + \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{4 \sqrt{114}}{9} + \frac{179}{27}} + \frac{25}{9 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{4 \sqrt{114}}{9} + \frac{179}{27}}}\right)\right) \left(x - \left(\frac{5}{3} + \frac{25}{9 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{4 \sqrt{114}}{9} + \frac{179}{27}}} + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{4 \sqrt{114}}{9} + \frac{179}{27}}\right)\right) \left(x - \left(\frac{25}{9 \sqrt[3]{\frac{4 \sqrt{114}}{9} + \frac{179}{27}}} + \frac{5}{3} + \sqrt[3]{\frac{4 \sqrt{114}}{9} + \frac{179}{27}}\right)\right)$$
(((1*(x - 3))*(x - (5/3 - (179/27 + 4*sqrt(114)/9)^(1/3)*(-1/2 - i*sqrt(3)/2) - 25/(9*(-1/2 - i*sqrt(3)/2)*(179/27 + 4*sqrt(114)/9)^(1/3)))))*(x - (5/3 - (179/27 + 4*sqrt(114)/9)^(1/3)*(-1/2 + i*sqrt(3)/2) - 25/(9*(-1/2 + i*sqrt(3)/2)*(179/27 + 4*sqrt(114)/9)^(1/3)))))*(x - (5/3 - (179/27 + 4*sqrt(114)/9)^(1/3) - 25/(9*(179/27 + 4*sqrt(114)/9)^(1/3))))
Общий знаменатель
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4 3 2 12 + x - 8*x - 4*x + 15*x
$$x^{4} - 8 x^{3} + 15 x^{2} - 4 x + 12$$
12 + x^4 - 8*x^3 - 4*x + 15*x^2
Рациональный знаменатель
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4 3 2 12 + x - 8*x - 4*x + 15*x
$$x^{4} - 8 x^{3} + 15 x^{2} - 4 x + 12$$
12 + x^4 - 8*x^3 - 4*x + 15*x^2