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Разложить многочлен на множители 2*x+5*x^8/8

Учитель очень удивится увидев твоё верное решение 😼

Примеры

Решение

Комбинаторика [src]
  /        7\
x*\16 + 5*x /
-------------
      8
x(5x7+16)8\frac{x \left(5 x^{7} + 16\right)}{8}
Разложение на множители [src]
  /       4/7  6/7    /pi\      4/7  6/7    /pi\\ /     4/7  6/7    2/pi\    4/7  6/7    2/pi\\ /     4/7  6/7    2/pi\    4/7  6/7    2/pi\        4/7  6/7    /pi\    /pi\\ /     4/7  6/7    /pi\    /2*pi\    4/7  6/7    /pi\    /2*pi\      4/7  6/7    /pi\    /2*pi\      4/7  6/7    /2*pi\    /pi\\ /       4/7  6/7    /pi\    /2*pi\    4/7  6/7    /pi\    /2*pi\      4/7  6/7    /pi\    /2*pi\      4/7  6/7    /2*pi\    /pi\\ /     4/7  6/7    /pi\    /3*pi\    4/7  6/7    /pi\    /3*pi\      4/7  6/7    /3*pi\    /pi\      4/7  6/7    /pi\    /3*pi\\ /     4/7  6/7    /pi\    /3*pi\    4/7  6/7    /pi\    /3*pi\      4/7  6/7    /pi\    /3*pi\      4/7  6/7    /3*pi\    /pi\\
  |      2   *5   *cos|--|   I*2   *5   *sin|--|| |    2   *5   *cos |--|   2   *5   *sin |--|| |    2   *5   *cos |--|   2   *5   *sin |--|   2*I*2   *5   *cos|--|*sin|--|| |    2   *5   *sin|--|*sin|----|   2   *5   *cos|--|*cos|----|   I*2   *5   *cos|--|*sin|----|   I*2   *5   *cos|----|*sin|--|| |      2   *5   *cos|--|*cos|----|   2   *5   *sin|--|*sin|----|   I*2   *5   *cos|--|*sin|----|   I*2   *5   *cos|----|*sin|--|| |    2   *5   *cos|--|*cos|----|   2   *5   *sin|--|*sin|----|   I*2   *5   *cos|----|*sin|--|   I*2   *5   *cos|--|*sin|----|| |    2   *5   *cos|--|*cos|----|   2   *5   *sin|--|*sin|----|   I*2   *5   *cos|--|*sin|----|   I*2   *5   *cos|----|*sin|--||
  |                   \7 /                  \7 /| |                  \7 /                 \7 /| |                  \7 /                 \7 /                    \7 /    \7 /| |                 \7 /    \ 7  /                \7 /    \ 7  /                  \7 /    \ 7  /                  \ 7  /    \7 /| |                   \7 /    \ 7  /                \7 /    \ 7  /                  \7 /    \ 7  /                  \ 7  /    \7 /| |                 \7 /    \ 7  /                \7 /    \ 7  /                  \ 7  /    \7 /                  \7 /    \ 7  /| |                 \7 /    \ 7  /                \7 /    \ 7  /                  \7 /    \ 7  /                  \ 7  /    \7 /|
x*|x + - ----------------- - -------------------|*|x + ------------------ + ------------------|*|x + ------------------ - ------------------ + -----------------------------|*|x + --------------------------- - --------------------------- - ----------------------------- - -----------------------------|*|x + - --------------------------- - --------------------------- + ----------------------------- - -----------------------------|*|x + --------------------------- + --------------------------- + ----------------------------- - -----------------------------|*|x + --------------------------- - --------------------------- + ----------------------------- + -----------------------------|
  \              5                    5         / \            5                    5         / \            5                    5                          5              / \                 5                             5                              5                               5              / \                   5                             5                              5                               5              / \                 5                             5                              5                               5              / \                 5                             5                              5                               5              /
x(x+(−247⋅567cos⁡(π7)5−247⋅567isin⁡(π7)5))(x+(247⋅567sin⁡2(π7)5+247⋅567cos⁡2(π7)5))(x+(−247⋅567sin⁡2(π7)5+247⋅567cos⁡2(π7)5+2⋅247⋅567isin⁡(π7)cos⁡(π7)5))(x+(−247⋅567cos⁡(π7)cos⁡(2π7)5+247⋅567sin⁡(π7)sin⁡(2π7)5−247⋅567isin⁡(2π7)cos⁡(π7)5−247⋅567isin⁡(π7)cos⁡(2π7)5))(x+(−247⋅567cos⁡(π7)cos⁡(2π7)5−247⋅567sin⁡(π7)sin⁡(2π7)5−247⋅567isin⁡(π7)cos⁡(2π7)5+247⋅567isin⁡(2π7)cos⁡(π7)5))(x+(247⋅567cos⁡(π7)cos⁡(3π7)5+247⋅567sin⁡(π7)sin⁡(3π7)5−247⋅567isin⁡(3π7)cos⁡(π7)5+247⋅567isin⁡(π7)cos⁡(3π7)5))(x+(−247⋅567sin⁡(π7)sin⁡(3π7)5+247⋅567cos⁡(π7)cos⁡(3π7)5+247⋅567isin⁡(π7)cos⁡(3π7)5+247⋅567isin⁡(3π7)cos⁡(π7)5))x \left(x + \left(- \frac{2^{\frac{4}{7}} \cdot 5^{\frac{6}{7}} \cos{\left(\frac{\pi}{7} \right)}}{5} - \frac{2^{\frac{4}{7}} \cdot 5^{\frac{6}{7}} i \sin{\left(\frac{\pi}{7} \right)}}{5}\right)\right) \left(x + \left(\frac{2^{\frac{4}{7}} \cdot 5^{\frac{6}{7}} \sin^{2}{\left(\frac{\pi}{7} \right)}}{5} + \frac{2^{\frac{4}{7}} \cdot 5^{\frac{6}{7}} \cos^{2}{\left(\frac{\pi}{7} \right)}}{5}\right)\right) \left(x + \left(- \frac{2^{\frac{4}{7}} \cdot 5^{\frac{6}{7}} \sin^{2}{\left(\frac{\pi}{7} \right)}}{5} + \frac{2^{\frac{4}{7}} \cdot 5^{\frac{6}{7}} \cos^{2}{\left(\frac{\pi}{7} \right)}}{5} + \frac{2 \cdot 2^{\frac{4}{7}} \cdot 5^{\frac{6}{7}} i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}}{5}\right)\right) \left(x + \left(- \frac{2^{\frac{4}{7}} \cdot 5^{\frac{6}{7}} \cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)}}{5} + \frac{2^{\frac{4}{7}} \cdot 5^{\frac{6}{7}} \sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{2 \pi}{7} \right)}}{5} - \frac{2^{\frac{4}{7}} \cdot 5^{\frac{6}{7}} i \sin{\left(\frac{2 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}}{5} - \frac{2^{\frac{4}{7}} \cdot 5^{\frac{6}{7}} i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)}}{5}\right)\right) \left(x + \left(- \frac{2^{\frac{4}{7}} \cdot 5^{\frac{6}{7}} \cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)}}{5} - \frac{2^{\frac{4}{7}} \cdot 5^{\frac{6}{7}} \sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{2 \pi}{7} \right)}}{5} - \frac{2^{\frac{4}{7}} \cdot 5^{\frac{6}{7}} i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{2 \pi}{7} \right)}}{5} + \frac{2^{\frac{4}{7}} \cdot 5^{\frac{6}{7}} i \sin{\left(\frac{2 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}}{5}\right)\right) \left(x + \left(\frac{2^{\frac{4}{7}} \cdot 5^{\frac{6}{7}} \cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)}}{5} + \frac{2^{\frac{4}{7}} \cdot 5^{\frac{6}{7}} \sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{3 \pi}{7} \right)}}{5} - \frac{2^{\frac{4}{7}} \cdot 5^{\frac{6}{7}} i \sin{\left(\frac{3 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}}{5} + \frac{2^{\frac{4}{7}} \cdot 5^{\frac{6}{7}} i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)}}{5}\right)\right) \left(x + \left(- \frac{2^{\frac{4}{7}} \cdot 5^{\frac{6}{7}} \sin{\left(\frac{\pi}{7} \right)} \sin{\left(\frac{3 \pi}{7} \right)}}{5} + \frac{2^{\frac{4}{7}} \cdot 5^{\frac{6}{7}} \cos{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)}}{5} + \frac{2^{\frac{4}{7}} \cdot 5^{\frac{6}{7}} i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{3 \pi}{7} \right)}}{5} + \frac{2^{\frac{4}{7}} \cdot 5^{\frac{6}{7}} i \sin{\left(\frac{3 \pi}{7} \right)} \cos{\left(\frac{\pi}{7} \right)}}{5}\right)\right)
Объединение рациональных выражений [src]
  /        7\
x*\16 + 5*x /
-------------
      8
x(5x7+16)8\frac{x \left(5 x^{7} + 16\right)}{8}