$$x \left(5 x^{3} + 6 x + 2\right)$$
Разложение на множители
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/ ________________ \ / ________________ \ / ________________ \
| / ____ / ___\ | | / ____ / ___\ | | / ____ |
| / 27 27*\/ 65 | 1 I*\/ 3 | | | / 27 27*\/ 65 | 1 I*\/ 3 | | | / 27 27*\/ 65 |
| 3 / -- + --------- *|- - - -------| | | 3 / -- + --------- *|- - + -------| | | 3 / -- + --------- |
| \/ 5 25 \ 2 2 / 6 | | \/ 5 25 \ 2 2 / 6 | | \/ 5 25 6 |
1*(x + 0)*|x + ------------------------------------- - ---------------------------------------|*|x + ------------------------------------- - ---------------------------------------|*|x + --------------------- - -----------------------|
| 3 ________________| | 3 ________________| | 3 ________________|
| / ___\ / ____ | | / ___\ / ____ | | / ____ |
| | 1 I*\/ 3 | / 27 27*\/ 65 | | | 1 I*\/ 3 | / 27 27*\/ 65 | | / 27 27*\/ 65 |
| 5*|- - - -------|*3 / -- + --------- | | 5*|- - + -------|*3 / -- + --------- | | 5*3 / -- + --------- |
\ \ 2 2 / \/ 5 25 / \ \ 2 2 / \/ 5 25 / \ \/ 5 25 /
$$1 \left(x + 0\right) \left(x + \left(\frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{5} + \frac{27 \sqrt{65}}{25}}}{3} - \frac{6}{5 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{5} + \frac{27 \sqrt{65}}{25}}}\right)\right) \left(x - \left(- \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{5} + \frac{27 \sqrt{65}}{25}}}{3} + \frac{6}{5 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{5} + \frac{27 \sqrt{65}}{25}}}\right)\right) \left(x - \left(- \frac{\sqrt[3]{\frac{27}{5} + \frac{27 \sqrt{65}}{25}}}{3} + \frac{6}{5 \sqrt[3]{\frac{27}{5} + \frac{27 \sqrt{65}}{25}}}\right)\right)$$
(((1*(x + 0))*(x + ((27/5 + 27*sqrt(65)/25)^(1/3)*(-1/2 - i*sqrt(3)/2)/3 - 6/(5*(-1/2 - i*sqrt(3)/2)*(27/5 + 27*sqrt(65)/25)^(1/3)))))*(x + ((27/5 + 27*sqrt(65)/25)^(1/3)*(-1/2 + i*sqrt(3)/2)/3 - 6/(5*(-1/2 + i*sqrt(3)/2)*(27/5 + 27*sqrt(65)/25)^(1/3)))))*(x + ((27/5 + 27*sqrt(65)/25)^(1/3)/3 - 6/(5*(27/5 + 27*sqrt(65)/25)^(1/3))))
Объединение рациональных выражений
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/ 3 / 2\\
x*\2 + 2*x + 3*x*\2 + x //
$$x \left(2 x^{3} + 3 x \left(x^{2} + 2\right) + 2\right)$$
x*(2 + 2*x^3 + 3*x*(2 + x^2))
2.0*x*(1.0 + x^3) + 3.0*x^2*(2.0 + x^2)
2.0*x*(1.0 + x^3) + 3.0*x^2*(2.0 + x^2)
$$x \left(5 x^{3} + 6 x + 2\right)$$
Рациональный знаменатель
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$$5 x^{4} + 6 x^{2} + 2 x$$
2 / 2\ / 3\
x *\6 + 3*x / + 2*x*\1 + x /
$$x^{2} \cdot \left(3 x^{2} + 6\right) + 2 x \left(x^{3} + 1\right)$$
x^2*(6 + 3*x^2) + 2*x*(1 + x^3)
$$5 x^{4} + 6 x^{2} + 2 x$$