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Разложить многочлен на множители P^9+64

Учитель очень удивится увидев твоё верное решение 😼

Примеры

Решение

Комбинаторика [src]
/     3\ /      6      3\
\4 + p /*\16 + p  - 4*p /
(p3+4)(p6−4p3+16)\left(p^{3} + 4\right) \left(p^{6} - 4 p^{3} + 16\right)
Разложение на множители [src]
                                                                                                                                           /     2/3    /pi\      2/3    /pi\    2/3   ___    /pi\      2/3   ___    /pi\\ /     2/3    /pi\    2/3   ___    /pi\      2/3    /pi\      2/3   ___    /pi\\                                                                                                                                                                                                                                                                                                                                                                                                                                                        
                                                                                                                                           |    2   *cos|--|   I*2   *sin|--|   2   *\/ 3 *sin|--|   I*2   *\/ 3 *cos|--|| |    2   *cos|--|   2   *\/ 3 *sin|--|   I*2   *sin|--|   I*2   *\/ 3 *cos|--||                                                                                                                                                                                                                                                                                                                                                                                                                                                        
/       2/3    /pi\      2/3    /pi\\ /     2/3    2/pi\    2/3    2/pi\\ /       2/3    2/pi\    2/3    2/pi\        2/3    /pi\    /pi\\ |            \9 /             \9 /                 \9 /                   \9 /| |            \9 /                 \9 /             \9 /                   \9 /| /       2/3    /pi\    /2*pi\    2/3    /pi\    /2*pi\      2/3    /pi\    /2*pi\      2/3    /2*pi\    /pi\\ /       2/3    /pi\    /2*pi\    2/3    /pi\    /2*pi\      2/3    /2*pi\    /pi\      2/3    /pi\    /2*pi\\ /       2/3    /pi\    /4*pi\    2/3    /pi\    /4*pi\      2/3    /pi\    /4*pi\      2/3    /4*pi\    /pi\\ /       2/3    /pi\    /4*pi\    2/3    /pi\    /4*pi\      2/3    /4*pi\    /pi\      2/3    /pi\    /4*pi\\
|p + - 2   *cos|--| - I*2   *sin|--||*|p + 2   *cos |--| + 2   *sin |--||*|p + - 2   *sin |--| + 2   *cos |--| + 2*I*2   *cos|--|*sin|--||*|p + ------------ + -------------- + ------------------ - --------------------|*|p + ------------ - ------------------ + -------------- + --------------------|*|p + - 2   *cos|--|*cos|----| + 2   *sin|--|*sin|----| - I*2   *cos|--|*sin|----| - I*2   *cos|----|*sin|--||*|p + - 2   *cos|--|*cos|----| - 2   *sin|--|*sin|----| - I*2   *cos|----|*sin|--| + I*2   *cos|--|*sin|----||*|p + - 2   *cos|--|*cos|----| + 2   *sin|--|*sin|----| - I*2   *cos|--|*sin|----| - I*2   *cos|----|*sin|--||*|p + - 2   *cos|--|*cos|----| - 2   *sin|--|*sin|----| - I*2   *cos|----|*sin|--| + I*2   *cos|--|*sin|----||
\              \9 /             \9 // \             \9 /            \9 // \               \9 /            \9 /               \9 /    \9 // \         2               2                  2                     2          / \         2                 2                  2                   2          / \              \9 /    \ 9  /           \9 /    \ 9  /             \9 /    \ 9  /             \ 9  /    \9 // \              \9 /    \ 9  /           \9 /    \ 9  /             \ 9  /    \9 /             \9 /    \ 9  // \              \9 /    \ 9  /           \9 /    \ 9  /             \9 /    \ 9  /             \ 9  /    \9 // \              \9 /    \ 9  /           \9 /    \ 9  /             \ 9  /    \9 /             \9 /    \ 9  //
(p+(223sin⁡2(π9)+223cos⁡2(π9)))(p+(−223cos⁡(π9)−223isin⁡(π9)))(p+(−223sin⁡2(π9)+223cos⁡2(π9)+2⋅223isin⁡(π9)cos⁡(π9)))(p+(2233sin⁡(π9)2+223cos⁡(π9)2−2233icos⁡(π9)2+223isin⁡(π9)2))(p+(−2233sin⁡(π9)2+223cos⁡(π9)2+223isin⁡(π9)2+2233icos⁡(π9)2))(p+(−223cos⁡(π9)cos⁡(2π9)+223sin⁡(π9)sin⁡(2π9)−223isin⁡(2π9)cos⁡(π9)−223isin⁡(π9)cos⁡(2π9)))(p+(−223cos⁡(π9)cos⁡(2π9)−223sin⁡(π9)sin⁡(2π9)−223isin⁡(π9)cos⁡(2π9)+223isin⁡(2π9)cos⁡(π9)))(p+(−223cos⁡(π9)cos⁡(4π9)+223sin⁡(π9)sin⁡(4π9)−223isin⁡(4π9)cos⁡(π9)−223isin⁡(π9)cos⁡(4π9)))(p+(−223sin⁡(π9)sin⁡(4π9)−223cos⁡(π9)cos⁡(4π9)−223isin⁡(π9)cos⁡(4π9)+223isin⁡(4π9)cos⁡(π9)))\left(p + \left(2^{\frac{2}{3}} \sin^{2}{\left(\frac{\pi}{9} \right)} + 2^{\frac{2}{3}} \cos^{2}{\left(\frac{\pi}{9} \right)}\right)\right) \left(p + \left(- 2^{\frac{2}{3}} \cos{\left(\frac{\pi}{9} \right)} - 2^{\frac{2}{3}} i \sin{\left(\frac{\pi}{9} \right)}\right)\right) \left(p + \left(- 2^{\frac{2}{3}} \sin^{2}{\left(\frac{\pi}{9} \right)} + 2^{\frac{2}{3}} \cos^{2}{\left(\frac{\pi}{9} \right)} + 2 \cdot 2^{\frac{2}{3}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}\right)\right) \left(p + \left(\frac{2^{\frac{2}{3}} \sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{2} + \frac{2^{\frac{2}{3}} \cos{\left(\frac{\pi}{9} \right)}}{2} - \frac{2^{\frac{2}{3}} \sqrt{3} i \cos{\left(\frac{\pi}{9} \right)}}{2} + \frac{2^{\frac{2}{3}} i \sin{\left(\frac{\pi}{9} \right)}}{2}\right)\right) \left(p + \left(- \frac{2^{\frac{2}{3}} \sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{2} + \frac{2^{\frac{2}{3}} \cos{\left(\frac{\pi}{9} \right)}}{2} + \frac{2^{\frac{2}{3}} i \sin{\left(\frac{\pi}{9} \right)}}{2} + \frac{2^{\frac{2}{3}} \sqrt{3} i \cos{\left(\frac{\pi}{9} \right)}}{2}\right)\right) \left(p + \left(- 2^{\frac{2}{3}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)} + 2^{\frac{2}{3}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{2 \pi}{9} \right)} - 2^{\frac{2}{3}} i \sin{\left(\frac{2 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)} - 2^{\frac{2}{3}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)}\right)\right) \left(p + \left(- 2^{\frac{2}{3}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)} - 2^{\frac{2}{3}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{2 \pi}{9} \right)} - 2^{\frac{2}{3}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{2 \pi}{9} \right)} + 2^{\frac{2}{3}} i \sin{\left(\frac{2 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}\right)\right) \left(p + \left(- 2^{\frac{2}{3}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)} + 2^{\frac{2}{3}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{4 \pi}{9} \right)} - 2^{\frac{2}{3}} i \sin{\left(\frac{4 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)} - 2^{\frac{2}{3}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)}\right)\right) \left(p + \left(- 2^{\frac{2}{3}} \sin{\left(\frac{\pi}{9} \right)} \sin{\left(\frac{4 \pi}{9} \right)} - 2^{\frac{2}{3}} \cos{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)} - 2^{\frac{2}{3}} i \sin{\left(\frac{\pi}{9} \right)} \cos{\left(\frac{4 \pi}{9} \right)} + 2^{\frac{2}{3}} i \sin{\left(\frac{4 \pi}{9} \right)} \cos{\left(\frac{\pi}{9} \right)}\right)\right)