Разложить многочлен на множители 16-t^40

Комбинаторика

 /      10\ /     10\ /     10      5\ /     10      5\
-\-2 + t  /*\2 + t  /*\2 + t   - 2*t /*\2 + t   + 2*t /

$$- \left(t^{10} - 2\right) \left(t^{10} + 2\right) \left(t^{10} - 2 t^{5} + 2\right) \left(t^{10} + 2 t^{5} + 2\right)$$

Разложение на множители

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                                                    /     3/5      3/5\ /     3/5      3/5\ /       3/5      3/5\ /       3/5      3/5\ |    10___   10___   ___               /       ___ | |    10___   10___   ___               /       ___ | |      10___   10___   ___               /       ___ | |      10___   10___   ___               /       ___ | |    10___   10___   ___               /       ___ | |    10___   10___   ___               /       ___ | |      10___   10___   ___               /       ___ | |      10___   10___   ___               /       ___ | |              /       ___      10___     10___   ___| |              /       ___      10___     10___   ___| |                /       ___      10___     10___   ___| |                /       ___      10___     10___   ___| |              /       ___      10___     10___   ___| |              /       ___      10___     10___   ___| |                /       ___      10___     10___   ___| |                /       ___      10___     10___   ___| |     3/5   2   *  /   - + -----       3/5    3/5   ___   I*2   *  /   - + -----       3/5   ___| |     3/5   2   *  /   - + -----       3/5    3/5   ___   I*2   *  /   - + -----       3/5   ___| |       3/5   2   *  /   - - -----       3/5    3/5   ___   I*2   *  /   - - -----       3/5   ___| |       3/5   2   *  /   - - -----       3/5    3/5   ___   I*2   *  /   - - -----       3/5   ___| |     3/5   2   *  /   - - -----     3/5   ___      3/5   I*2   *  /   - - -----       3/5   ___| |     3/5   2   *  /   - - -----       3/5    3/5   ___   I*2   *  /   - - -----       3/5   ___| |       3/5   2   *  /   - + -----       3/5    3/5   ___   I*2   *  /   - + -----       3/5   ___| |       3/5   2   *  /   - + -----     3/5   ___      3/5   I*2   *  /   - + -----       3/5   ___| |       3/5   2   *  /   - - -----       3/5    3/5   ___   I*2   *  /   - - -----       3/5   ___| |       3/5   2   *  /   - - -----       3/5    3/5   ___   I*2   *  /   - - -----       3/5   ___| |     3/5   2   *  /   - - -----       3/5    3/5   ___   I*2   *  /   - - -----       3/5   ___| |     3/5   2   *  /   - - -----     3/5   ___      3/5   I*2   *  /   - - -----       3/5   ___| |     3/5   2   *  /   - + -----       3/5    3/5   ___   I*2   *  /   - + -----       3/5   ___| |     3/5   2   *  /   - + -----       3/5    3/5   ___   I*2   *  /   - + -----       3/5   ___| |       3/5   2   *  /   - + -----     3/5   ___      3/5   I*2   *  /   - + -----       3/5   ___| |       3/5   2   *  /   - + -----       3/5    3/5   ___   I*2   *  /   - + -----       3/5   ___|
/    10___\ /    10___\ /      10___\ /      10___\ |    2      I*2   | |    2      I*2   | |      2      I*2   | |      2      I*2   | |    \/ 2    \/ 2 *\/ 5      10___    /  5   \/ 5  | |    \/ 2    \/ 2 *\/ 5      10___    /  5   \/ 5  | |      \/ 2    \/ 2 *\/ 5      10___    /  5   \/ 5  | |      \/ 2    \/ 2 *\/ 5      10___    /  5   \/ 5  | |    \/ 2    \/ 2 *\/ 5      10___    /  5   \/ 5  | |    \/ 2    \/ 2 *\/ 5      10___    /  5   \/ 5  | |      \/ 2    \/ 2 *\/ 5      10___    /  5   \/ 5  | |      \/ 2    \/ 2 *\/ 5      10___    /  5   \/ 5  | |    10___    /  5   \/ 5     I*\/ 2    I*\/ 2 *\/ 5 | |    10___    /  5   \/ 5     I*\/ 2    I*\/ 2 *\/ 5 | |      10___    /  5   \/ 5     I*\/ 2    I*\/ 2 *\/ 5 | |      10___    /  5   \/ 5     I*\/ 2    I*\/ 2 *\/ 5 | |    10___    /  5   \/ 5     I*\/ 2    I*\/ 2 *\/ 5 | |    10___    /  5   \/ 5     I*\/ 2    I*\/ 2 *\/ 5 | |      10___    /  5   \/ 5     I*\/ 2    I*\/ 2 *\/ 5 | |      10___    /  5   \/ 5     I*\/ 2    I*\/ 2 *\/ 5 | |    2           \/    8     8      I*2      2   *\/ 5           \/    8     8      I*2   *\/ 5 | |    2           \/    8     8      I*2      2   *\/ 5           \/    8     8      I*2   *\/ 5 | |      2           \/    8     8      I*2      2   *\/ 5           \/    8     8      I*2   *\/ 5 | |      2           \/    8     8      I*2      2   *\/ 5           \/    8     8      I*2   *\/ 5 | |    2           \/    8     8      2   *\/ 5    I*2             \/    8     8      I*2   *\/ 5 | |    2           \/    8     8      I*2      2   *\/ 5           \/    8     8      I*2   *\/ 5 | |      2           \/    8     8      I*2      2   *\/ 5           \/    8     8      I*2   *\/ 5 | |      2           \/    8     8      2   *\/ 5    I*2             \/    8     8      I*2   *\/ 5 | |      2           \/    8     8      I*2      2   *\/ 5           \/    8     8      I*2   *\/ 5 | |      2           \/    8     8      I*2      2   *\/ 5           \/    8     8      I*2   *\/ 5 | |    2           \/    8     8      I*2      2   *\/ 5           \/    8     8      I*2   *\/ 5 | |    2           \/    8     8      2   *\/ 5    I*2             \/    8     8      I*2   *\/ 5 | |    2           \/    8     8      I*2      2   *\/ 5           \/    8     8      I*2   *\/ 5 | |    2           \/    8     8      I*2      2   *\/ 5           \/    8     8      I*2   *\/ 5 | |      2           \/    8     8      2   *\/ 5    I*2             \/    8     8      I*2   *\/ 5 | |      2           \/    8     8      I*2      2   *\/ 5           \/    8     8      I*2   *\/ 5 |
\t + \/ 2 /*\t - \/ 2 /*\t + I*\/ 2 /*\t - I*\/ 2 /*|t + ---- + ------|*|t + ---- - ------|*|t + - ---- + ------|*|t + - ---- - ------|*|t + ----- - ----------- + I*\/ 2 *  /   - + ----- |*|t + ----- - ----------- - I*\/ 2 *  /   - + ----- |*|t + - ----- - ----------- + I*\/ 2 *  /   - - ----- |*|t + - ----- - ----------- - I*\/ 2 *  /   - - ----- |*|t + ----- + ----------- + I*\/ 2 *  /   - - ----- |*|t + ----- + ----------- - I*\/ 2 *  /   - - ----- |*|t + - ----- + ----------- + I*\/ 2 *  /   - + ----- |*|t + - ----- + ----------- - I*\/ 2 *  /   - + ----- |*|t + \/ 2 *  /   - - -----  - ------- - -------------|*|t + \/ 2 *  /   - - -----  + ------- + -------------|*|t + - \/ 2 *  /   - - -----  - ------- - -------------|*|t + - \/ 2 *  /   - - -----  + ------- + -------------|*|t + \/ 2 *  /   - + -----  + ------- - -------------|*|t + \/ 2 *  /   - + -----  - ------- + -------------|*|t + - \/ 2 *  /   - + -----  + ------- - -------------|*|t + - \/ 2 *  /   - + -----  - ------- + -------------|*|t + ---- - --------------------- - ------ - ---------- - ----------------------- + ------------|*|t + ---- - --------------------- + ------ - ---------- + ----------------------- - ------------|*|t + - ---- - --------------------- + ------ - ---------- - ----------------------- + ------------|*|t + - ---- - --------------------- - ------ - ---------- + ----------------------- - ------------|*|t + ---- - --------------------- + ---------- - ------ - ----------------------- - ------------|*|t + ---- - --------------------- + ------ + ---------- + ----------------------- + ------------|*|t + - ---- - --------------------- + ------ + ---------- - ----------------------- - ------------|*|t + - ---- - --------------------- + ---------- - ------ + ----------------------- + ------------|*|t + - ---- + --------------------- - ------ - ---------- - ----------------------- - ------------|*|t + - ---- + --------------------- + ------ - ---------- + ----------------------- + ------------|*|t + ---- + --------------------- + ------ + ---------- - ----------------------- + ------------|*|t + ---- + --------------------- + ---------- - ------ + ----------------------- - ------------|*|t + ---- + --------------------- + ------ - ---------- - ----------------------- - ------------|*|t + ---- + --------------------- - ------ - ---------- + ----------------------- + ------------|*|t + - ---- + --------------------- + ---------- - ------ - ----------------------- + ------------|*|t + - ---- + --------------------- + ------ + ---------- + ----------------------- - ------------|
                                                    \     2       2   / \     2       2   / \       2       2   / \       2       2   / \      4          4                \/    8     8   / \      4          4                \/    8     8   / \        4          4                \/    8     8   / \        4          4                \/    8     8   / \      4          4                \/    8     8   / \      4          4                \/    8     8   / \        4          4                \/    8     8   / \        4          4                \/    8     8   / \          \/    8     8         4            4      / \          \/    8     8         4            4      / \            \/    8     8         4            4      / \            \/    8     8         4            4      / \          \/    8     8         4            4      / \          \/    8     8         4            4      / \            \/    8     8         4            4      / \            \/    8     8         4            4      / \     8               2               8          8                   2                   8      / \     8               2               8          8                   2                   8      / \       8               2               8          8                   2                   8      / \       8               2               8          8                   2                   8      / \     8               2                 8          8                 2                   8      / \     8               2               8          8                   2                   8      / \       8               2               8          8                   2                   8      / \       8               2                 8          8                 2                   8      / \       8               2               8          8                   2                   8      / \       8               2               8          8                   2                   8      / \     8               2               8          8                   2                   8      / \     8               2                 8          8                 2                   8      / \     8               2               8          8                   2                   8      / \     8               2               8          8                   2                   8      / \       8               2                 8          8                 2                   8      / \       8               2               8          8                   2                   8      /

$$\left(t - \sqrt[10]{2}\right) \left(t + \sqrt[10]{2}\right) \left(t + \sqrt[10]{2} i\right) \left(t - \sqrt[10]{2} i\right) \left(t + \left(\frac{2^{\frac{3}{5}}}{2} + \frac{2^{\frac{3}{5}} i}{2}\right)\right) \left(t + \left(\frac{2^{\frac{3}{5}}}{2} - \frac{2^{\frac{3}{5}} i}{2}\right)\right) \left(t + \left(- \frac{2^{\frac{3}{5}}}{2} + \frac{2^{\frac{3}{5}} i}{2}\right)\right) \left(t + \left(- \frac{2^{\frac{3}{5}}}{2} - \frac{2^{\frac{3}{5}} i}{2}\right)\right) \left(t + \left(- \frac{\sqrt[10]{2} \sqrt{5}}{4} + \frac{\sqrt[10]{2}}{4} + \sqrt[10]{2} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(t + \left(- \frac{\sqrt[10]{2} \sqrt{5}}{4} + \frac{\sqrt[10]{2}}{4} - \sqrt[10]{2} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(t + \left(- \frac{\sqrt[10]{2} \sqrt{5}}{4} - \frac{\sqrt[10]{2}}{4} + \sqrt[10]{2} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(t + \left(- \frac{\sqrt[10]{2} \sqrt{5}}{4} - \frac{\sqrt[10]{2}}{4} - \sqrt[10]{2} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(t + \left(\frac{\sqrt[10]{2}}{4} + \frac{\sqrt[10]{2} \sqrt{5}}{4} + \sqrt[10]{2} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(t + \left(\frac{\sqrt[10]{2}}{4} + \frac{\sqrt[10]{2} \sqrt{5}}{4} - \sqrt[10]{2} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(t + \left(- \frac{\sqrt[10]{2}}{4} + \frac{\sqrt[10]{2} \sqrt{5}}{4} + \sqrt[10]{2} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(t + \left(- \frac{\sqrt[10]{2}}{4} + \frac{\sqrt[10]{2} \sqrt{5}}{4} - \sqrt[10]{2} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(t + \left(\sqrt[10]{2} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} - \frac{\sqrt[10]{2} \sqrt{5} i}{4} - \frac{\sqrt[10]{2} i}{4}\right)\right) \left(t + \left(\sqrt[10]{2} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} + \frac{\sqrt[10]{2} i}{4} + \frac{\sqrt[10]{2} \sqrt{5} i}{4}\right)\right) \left(t + \left(- \sqrt[10]{2} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} - \frac{\sqrt[10]{2} \sqrt{5} i}{4} - \frac{\sqrt[10]{2} i}{4}\right)\right) \left(t + \left(- \sqrt[10]{2} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} + \frac{\sqrt[10]{2} i}{4} + \frac{\sqrt[10]{2} \sqrt{5} i}{4}\right)\right) \left(t + \left(\sqrt[10]{2} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} - \frac{\sqrt[10]{2} \sqrt{5} i}{4} + \frac{\sqrt[10]{2} i}{4}\right)\right) \left(t + \left(\sqrt[10]{2} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} - \frac{\sqrt[10]{2} i}{4} + \frac{\sqrt[10]{2} \sqrt{5} i}{4}\right)\right) \left(t + \left(- \sqrt[10]{2} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} - \frac{\sqrt[10]{2} \sqrt{5} i}{4} + \frac{\sqrt[10]{2} i}{4}\right)\right) \left(t + \left(- \sqrt[10]{2} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} - \frac{\sqrt[10]{2} i}{4} + \frac{\sqrt[10]{2} \sqrt{5} i}{4}\right)\right) \left(t + \left(- \frac{2^{\frac{3}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2} - \frac{2^{\frac{3}{5}} \sqrt{5}}{8} + \frac{2^{\frac{3}{5}}}{8} - \frac{2^{\frac{3}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2} - \frac{2^{\frac{3}{5}} i}{8} + \frac{2^{\frac{3}{5}} \sqrt{5} i}{8}\right)\right) \left(t + \left(- \frac{2^{\frac{3}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2} - \frac{2^{\frac{3}{5}} \sqrt{5}}{8} + \frac{2^{\frac{3}{5}}}{8} - \frac{2^{\frac{3}{5}} \sqrt{5} i}{8} + \frac{2^{\frac{3}{5}} i}{8} + \frac{2^{\frac{3}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2}\right)\right) \left(t + \left(- \frac{2^{\frac{3}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} - \frac{2^{\frac{3}{5}} \sqrt{5}}{8} - \frac{2^{\frac{3}{5}}}{8} - \frac{2^{\frac{3}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} + \frac{2^{\frac{3}{5}} i}{8} + \frac{2^{\frac{3}{5}} \sqrt{5} i}{8}\right)\right) \left(t + \left(- \frac{2^{\frac{3}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} - \frac{2^{\frac{3}{5}} \sqrt{5}}{8} - \frac{2^{\frac{3}{5}}}{8} - \frac{2^{\frac{3}{5}} \sqrt{5} i}{8} - \frac{2^{\frac{3}{5}} i}{8} + \frac{2^{\frac{3}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2}\right)\right) \left(t + \left(- \frac{2^{\frac{3}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} + \frac{2^{\frac{3}{5}}}{8} + \frac{2^{\frac{3}{5}} \sqrt{5}}{8} - \frac{2^{\frac{3}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} - \frac{2^{\frac{3}{5}} \sqrt{5} i}{8} - \frac{2^{\frac{3}{5}} i}{8}\right)\right) \left(t + \left(- \frac{2^{\frac{3}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} + \frac{2^{\frac{3}{5}}}{8} + \frac{2^{\frac{3}{5}} \sqrt{5}}{8} + \frac{2^{\frac{3}{5}} i}{8} + \frac{2^{\frac{3}{5}} \sqrt{5} i}{8} + \frac{2^{\frac{3}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2}\right)\right) \left(t + \left(- \frac{2^{\frac{3}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2} - \frac{2^{\frac{3}{5}}}{8} + \frac{2^{\frac{3}{5}} \sqrt{5}}{8} - \frac{2^{\frac{3}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2} - \frac{2^{\frac{3}{5}} \sqrt{5} i}{8} + \frac{2^{\frac{3}{5}} i}{8}\right)\right) \left(t + \left(- \frac{2^{\frac{3}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2} - \frac{2^{\frac{3}{5}}}{8} + \frac{2^{\frac{3}{5}} \sqrt{5}}{8} - \frac{2^{\frac{3}{5}} i}{8} + \frac{2^{\frac{3}{5}} \sqrt{5} i}{8} + \frac{2^{\frac{3}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2}\right)\right) \left(t + \left(- \frac{2^{\frac{3}{5}} \sqrt{5}}{8} - \frac{2^{\frac{3}{5}}}{8} + \frac{2^{\frac{3}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} - \frac{2^{\frac{3}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} - \frac{2^{\frac{3}{5}} \sqrt{5} i}{8} - \frac{2^{\frac{3}{5}} i}{8}\right)\right) \left(t + \left(- \frac{2^{\frac{3}{5}} \sqrt{5}}{8} - \frac{2^{\frac{3}{5}}}{8} + \frac{2^{\frac{3}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} + \frac{2^{\frac{3}{5}} i}{8} + \frac{2^{\frac{3}{5}} \sqrt{5} i}{8} + \frac{2^{\frac{3}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2}\right)\right) \left(t + \left(\frac{2^{\frac{3}{5}}}{8} + \frac{2^{\frac{3}{5}} \sqrt{5}}{8} + \frac{2^{\frac{3}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} - \frac{2^{\frac{3}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} + \frac{2^{\frac{3}{5}} i}{8} + \frac{2^{\frac{3}{5}} \sqrt{5} i}{8}\right)\right) \left(t + \left(\frac{2^{\frac{3}{5}}}{8} + \frac{2^{\frac{3}{5}} \sqrt{5}}{8} + \frac{2^{\frac{3}{5}} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2} - \frac{2^{\frac{3}{5}} \sqrt{5} i}{8} - \frac{2^{\frac{3}{5}} i}{8} + \frac{2^{\frac{3}{5}} i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{2}\right)\right) \left(t + \left(- \frac{2^{\frac{3}{5}} \sqrt{5}}{8} + \frac{2^{\frac{3}{5}}}{8} + \frac{2^{\frac{3}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2} - \frac{2^{\frac{3}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2} - \frac{2^{\frac{3}{5}} \sqrt{5} i}{8} + \frac{2^{\frac{3}{5}} i}{8}\right)\right) \left(t + \left(- \frac{2^{\frac{3}{5}} \sqrt{5}}{8} + \frac{2^{\frac{3}{5}}}{8} + \frac{2^{\frac{3}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2} - \frac{2^{\frac{3}{5}} i}{8} + \frac{2^{\frac{3}{5}} \sqrt{5} i}{8} + \frac{2^{\frac{3}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2}\right)\right) \left(t + \left(- \frac{2^{\frac{3}{5}}}{8} + \frac{2^{\frac{3}{5}} \sqrt{5}}{8} + \frac{2^{\frac{3}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2} - \frac{2^{\frac{3}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2} - \frac{2^{\frac{3}{5}} i}{8} + \frac{2^{\frac{3}{5}} \sqrt{5} i}{8}\right)\right) \left(t + \left(- \frac{2^{\frac{3}{5}}}{8} + \frac{2^{\frac{3}{5}} \sqrt{5}}{8} + \frac{2^{\frac{3}{5}} \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2} - \frac{2^{\frac{3}{5}} \sqrt{5} i}{8} + \frac{2^{\frac{3}{5}} i}{8} + \frac{2^{\frac{3}{5}} i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}{2}\right)\right)$$