1. 2. 3. 4. 5. 6. Разложить на множители 256-t^36 (256 минус t в кубе 6) - многочлен [Есть ответ!]

Разложить многочлен на множители 256-t^36

Учитель очень удивится увидев твоё верное решение😼

Решение

Комбинаторика [src]
 /      9\ /     9\ /      18\
-\-4 + t /*\4 + t /*\16 + t  /
$$- \left(t^{9} - 4\right) \left(t^{9} + 4\right) \left(t^{18} + 16\right)$$
Разложение на множители [src]
                                                /     2/9      2/9   ___\ /     2/9      2/9   ___\ /       2/9      2/9   ___\ /       2/9      2/9   ___\ /       2/9    2/9   ___\ /         2/9    2/9   ___\ /       2/9   ___      2/9\ /         2/9    2/9   ___\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        
/     2/9\ /     2/9\ /       2/9\ /       2/9\ |    2      I*2   *\/ 3 | |    2      I*2   *\/ 3 | |      2      I*2   *\/ 3 | |      2      I*2   *\/ 3 | |    I*2      2   *\/ 3 | |      I*2      2   *\/ 3 | |      2   *\/ 3    I*2   | |      I*2      2   *\/ 3 | /     2/9    /pi\      2/9    /pi\\ /     2/9    /pi\      2/9    /pi\\ /       2/9    /pi\      2/9    /pi\\ /       2/9    /pi\      2/9    /pi\\ /     2/9    /pi\      2/9    /pi\\ /     2/9    /pi\      2/9    /pi\\ /       2/9    /pi\      2/9    /pi\\ /       2/9    /pi\      2/9    /pi\\ /     2/9    /2*pi\      2/9    /2*pi\\ /     2/9    /2*pi\      2/9    /2*pi\\ /       2/9    /2*pi\      2/9    /2*pi\\ /       2/9    /2*pi\      2/9    /2*pi\\ /     2/9    /5*pi\      2/9    /5*pi\\ /     2/9    /5*pi\      2/9    /5*pi\\ /       2/9    /5*pi\      2/9    /5*pi\\ /       2/9    /5*pi\      2/9    /5*pi\\ /     2/9    /7*pi\      2/9    /7*pi\\ /     2/9    /7*pi\      2/9    /7*pi\\ /       2/9    /7*pi\      2/9    /7*pi\\ /       2/9    /7*pi\      2/9    /7*pi\\ /     2/9    /4*pi\      2/9    /4*pi\\ /     2/9    /4*pi\      2/9    /4*pi\\ /       2/9    /4*pi\      2/9    /4*pi\\ /       2/9    /4*pi\      2/9    /4*pi\\
\t + 2   /*\t - 2   /*\t + I*2   /*\t - I*2   /*|t + ---- + ------------|*|t + ---- - ------------|*|t + - ---- + ------------|*|t + - ---- - ------------|*|t + ------ + ----------|*|t + - ------ + ----------|*|t + - ---------- + ------|*|t + - ------ - ----------|*|t + 2   *cos|--| + I*2   *sin|--||*|t + 2   *cos|--| - I*2   *sin|--||*|t + - 2   *cos|--| + I*2   *sin|--||*|t + - 2   *cos|--| - I*2   *sin|--||*|t + 2   *cos|--| + I*2   *sin|--||*|t + 2   *cos|--| - I*2   *sin|--||*|t + - 2   *cos|--| + I*2   *sin|--||*|t + - 2   *cos|--| - I*2   *sin|--||*|t + 2   *cos|----| + I*2   *sin|----||*|t + 2   *cos|----| - I*2   *sin|----||*|t + - 2   *cos|----| + I*2   *sin|----||*|t + - 2   *cos|----| - I*2   *sin|----||*|t + 2   *cos|----| + I*2   *sin|----||*|t + 2   *cos|----| - I*2   *sin|----||*|t + - 2   *cos|----| + I*2   *sin|----||*|t + - 2   *cos|----| - I*2   *sin|----||*|t + 2   *cos|----| + I*2   *sin|----||*|t + 2   *cos|----| - I*2   *sin|----||*|t + - 2   *cos|----| + I*2   *sin|----||*|t + - 2   *cos|----| - I*2   *sin|----||*|t + 2   *cos|----| + I*2   *sin|----||*|t + 2   *cos|----| - I*2   *sin|----||*|t + - 2   *cos|----| + I*2   *sin|----||*|t + - 2   *cos|----| - I*2   *sin|----||
                                                \     2          2      / \     2          2      / \       2          2      / \       2          2      / \      2          2     / \        2          2     / \          2          2   / \        2          2     / \            \18/             \18// \            \18/             \18// \              \18/             \18// \              \18/             \18// \            \9 /             \9 // \            \9 /             \9 // \              \9 /             \9 // \              \9 /             \9 // \            \ 9  /             \ 9  // \            \ 9  /             \ 9  // \              \ 9  /             \ 9  // \              \ 9  /             \ 9  // \            \ 18 /             \ 18 // \            \ 18 /             \ 18 // \              \ 18 /             \ 18 // \              \ 18 /             \ 18 // \            \ 18 /             \ 18 // \            \ 18 /             \ 18 // \              \ 18 /             \ 18 // \              \ 18 /             \ 18 // \            \ 9  /             \ 9  // \            \ 9  /             \ 9  // \              \ 9  /             \ 9  // \              \ 9  /             \ 9  //
$$\left(t - 2^{\frac{2}{9}}\right) \left(t + 2^{\frac{2}{9}}\right) \left(t + 2^{\frac{2}{9}} i\right) \left(t - 2^{\frac{2}{9}} i\right) \left(t + \left(\frac{2^{\frac{2}{9}}}{2} + \frac{2^{\frac{2}{9}} \sqrt{3} i}{2}\right)\right) \left(t + \left(\frac{2^{\frac{2}{9}}}{2} - \frac{2^{\frac{2}{9}} \sqrt{3} i}{2}\right)\right) \left(t + \left(- \frac{2^{\frac{2}{9}}}{2} + \frac{2^{\frac{2}{9}} \sqrt{3} i}{2}\right)\right) \left(t + \left(- \frac{2^{\frac{2}{9}}}{2} - \frac{2^{\frac{2}{9}} \sqrt{3} i}{2}\right)\right) \left(t + \left(\frac{2^{\frac{2}{9}} \sqrt{3}}{2} + \frac{2^{\frac{2}{9}} i}{2}\right)\right) \left(t + \left(\frac{2^{\frac{2}{9}} \sqrt{3}}{2} - \frac{2^{\frac{2}{9}} i}{2}\right)\right) \left(t + \left(- \frac{2^{\frac{2}{9}} \sqrt{3}}{2} + \frac{2^{\frac{2}{9}} i}{2}\right)\right) \left(t + \left(- \frac{2^{\frac{2}{9}} \sqrt{3}}{2} - \frac{2^{\frac{2}{9}} i}{2}\right)\right) \left(t + \left(2^{\frac{2}{9}} \cos{\left(\frac{\pi}{18} \right)} + 2^{\frac{2}{9}} i \sin{\left(\frac{\pi}{18} \right)}\right)\right) \left(t + \left(2^{\frac{2}{9}} \cos{\left(\frac{\pi}{18} \right)} - 2^{\frac{2}{9}} i \sin{\left(\frac{\pi}{18} \right)}\right)\right) \left(t + \left(- 2^{\frac{2}{9}} \cos{\left(\frac{\pi}{18} \right)} + 2^{\frac{2}{9}} i \sin{\left(\frac{\pi}{18} \right)}\right)\right) \left(t + \left(- 2^{\frac{2}{9}} \cos{\left(\frac{\pi}{18} \right)} - 2^{\frac{2}{9}} i \sin{\left(\frac{\pi}{18} \right)}\right)\right) \left(t + \left(2^{\frac{2}{9}} \cos{\left(\frac{\pi}{9} \right)} + 2^{\frac{2}{9}} i \sin{\left(\frac{\pi}{9} \right)}\right)\right) \left(t + \left(2^{\frac{2}{9}} \cos{\left(\frac{\pi}{9} \right)} - 2^{\frac{2}{9}} i \sin{\left(\frac{\pi}{9} \right)}\right)\right) \left(t + \left(- 2^{\frac{2}{9}} \cos{\left(\frac{\pi}{9} \right)} + 2^{\frac{2}{9}} i \sin{\left(\frac{\pi}{9} \right)}\right)\right) \left(t + \left(- 2^{\frac{2}{9}} \cos{\left(\frac{\pi}{9} \right)} - 2^{\frac{2}{9}} i \sin{\left(\frac{\pi}{9} \right)}\right)\right) \left(t + \left(2^{\frac{2}{9}} \cos{\left(\frac{2 \pi}{9} \right)} + 2^{\frac{2}{9}} i \sin{\left(\frac{2 \pi}{9} \right)}\right)\right) \left(t + \left(2^{\frac{2}{9}} \cos{\left(\frac{2 \pi}{9} \right)} - 2^{\frac{2}{9}} i \sin{\left(\frac{2 \pi}{9} \right)}\right)\right) \left(t + \left(- 2^{\frac{2}{9}} \cos{\left(\frac{2 \pi}{9} \right)} + 2^{\frac{2}{9}} i \sin{\left(\frac{2 \pi}{9} \right)}\right)\right) \left(t + \left(- 2^{\frac{2}{9}} \cos{\left(\frac{2 \pi}{9} \right)} - 2^{\frac{2}{9}} i \sin{\left(\frac{2 \pi}{9} \right)}\right)\right) \left(t + \left(2^{\frac{2}{9}} \cos{\left(\frac{5 \pi}{18} \right)} + 2^{\frac{2}{9}} i \sin{\left(\frac{5 \pi}{18} \right)}\right)\right) \left(t + \left(2^{\frac{2}{9}} \cos{\left(\frac{5 \pi}{18} \right)} - 2^{\frac{2}{9}} i \sin{\left(\frac{5 \pi}{18} \right)}\right)\right) \left(t + \left(- 2^{\frac{2}{9}} \cos{\left(\frac{5 \pi}{18} \right)} + 2^{\frac{2}{9}} i \sin{\left(\frac{5 \pi}{18} \right)}\right)\right) \left(t + \left(- 2^{\frac{2}{9}} \cos{\left(\frac{5 \pi}{18} \right)} - 2^{\frac{2}{9}} i \sin{\left(\frac{5 \pi}{18} \right)}\right)\right) \left(t + \left(2^{\frac{2}{9}} \cos{\left(\frac{7 \pi}{18} \right)} + 2^{\frac{2}{9}} i \sin{\left(\frac{7 \pi}{18} \right)}\right)\right) \left(t + \left(2^{\frac{2}{9}} \cos{\left(\frac{7 \pi}{18} \right)} - 2^{\frac{2}{9}} i \sin{\left(\frac{7 \pi}{18} \right)}\right)\right) \left(t + \left(- 2^{\frac{2}{9}} \cos{\left(\frac{7 \pi}{18} \right)} + 2^{\frac{2}{9}} i \sin{\left(\frac{7 \pi}{18} \right)}\right)\right) \left(t + \left(- 2^{\frac{2}{9}} \cos{\left(\frac{7 \pi}{18} \right)} - 2^{\frac{2}{9}} i \sin{\left(\frac{7 \pi}{18} \right)}\right)\right) \left(t + \left(2^{\frac{2}{9}} \cos{\left(\frac{4 \pi}{9} \right)} + 2^{\frac{2}{9}} i \sin{\left(\frac{4 \pi}{9} \right)}\right)\right) \left(t + \left(2^{\frac{2}{9}} \cos{\left(\frac{4 \pi}{9} \right)} - 2^{\frac{2}{9}} i \sin{\left(\frac{4 \pi}{9} \right)}\right)\right) \left(t + \left(- 2^{\frac{2}{9}} \cos{\left(\frac{4 \pi}{9} \right)} + 2^{\frac{2}{9}} i \sin{\left(\frac{4 \pi}{9} \right)}\right)\right) \left(t + \left(- 2^{\frac{2}{9}} \cos{\left(\frac{4 \pi}{9} \right)} - 2^{\frac{2}{9}} i \sin{\left(\frac{4 \pi}{9} \right)}\right)\right)$$