Mister Exam
Factor polynomial y^2/2+y^23/23
The solution
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[src]
2 23 y y -- + --- 2 23
$$\frac{y^{23}}{23} + \frac{y^{2}}{2}$$
y^2/2 + y^23/23
Fraction decomposition
[src]
y^2/2 + y^23/23
$$\frac{y^{23}}{23} + \frac{y^{2}}{2}$$
2 23 y y -- + --- 2 23
Factorization
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21 21____ /pi\ /2*pi\ 21 21____ /2*pi\ /pi\ 21 21____ /pi\ /2*pi\| | 21 21____ /pi\ /4*pi\ 21 21____ /pi\ /4*pi\ 21 21____ /pi\ /4*pi\ 21 21____ /4*pi\ /pi\| | 21 21____ /pi\ /4*pi\ 21 21____ /pi\ /4*pi\ 21 21____ /4*pi\ /pi\ 21 21____ /pi\ /4*pi\| | 21 21____ /pi\ /2*pi\ 21 21____ /pi\ /2*pi\ 21 21____ /pi\ /2*pi\ 21 21____ /2*pi\ /pi\| | 21 21____ /pi\ /2*pi\ 21 21____ /pi\ /2*pi\ 21 21____ /2*pi\ /pi\ 21 21____ /pi\ /2*pi\| | 21 21____ /pi\ /8*pi\ 21 21____ /pi\ /8*pi\ 21 21____ /pi\ /8*pi\ 21 21____ /8*pi\ /pi\| | 21 21____ /pi\ /8*pi\ 21 21____ /pi\ /8*pi\ 21 21____ /8*pi\ /pi\ 21 21____ /pi\ /8*pi\| | 21 21____ /pi\ /10*pi\ 21 21____ /pi\ /10*pi\ 21 21____ /pi\ /10*pi\ 21 21____ /10*pi\ /pi\| | 21 21____ /pi\ /pi\ 21 21____ /pi\ /pi\ 21 21____ /pi\ /pi\ 21 21____ /pi\ /pi\| | 21 21____ /pi\ /pi\ 21 21____ /pi\ /pi\ 21 21____ /pi\ /pi\ 21 21____ /pi\ /pi\| | 21 21____ /pi\ /5*pi\ 21 21____ /pi\ /5*pi\ 21 21____ /pi\ /5*pi\ 21 21____ /5*pi\ /pi\| | 21 21____ /pi\ /5*pi\ 21 21____ /pi\ /5*pi\ 21 21____ /pi\ /5*pi\ 21 21____ /5*pi\ /pi\| | 21 21____ /pi\ /3*pi\ 21 21____ /pi\ /3*pi\ 21 21____ /pi\ /3*pi\ 21 21____ /3*pi\ /pi\| | 21 21____ /pi\ /3*pi\ 21 21____ /pi\ /3*pi\ 21 21____ /pi\ /3*pi\ 21 21____ /3*pi\ /pi\| | 21 21____ /pi\ /10*pi\ 21 21____ /pi\ /10*pi\ 21 21____ /10*pi\ /pi\ 21 21____ /pi\ /10*pi\| | 2 *\/ 23 *cos|--| I*2 *\/ 23 *sin|--|| | 2 *\/ 23 *cos |--| 2 *\/ 23 *sin |--|| | 2 *\/ 23 *sin |--| 2 *\/ 23 *cos |--| -- | | 2 *\/ 23 *cos|--| I*2 *\/ 23 *sin|--| 2 *\/ 3 *\/ 23 *sin|--| I*2 *\/ 3 *\/ 23 *cos|--|| | 2 *\/ 23 *cos|--| I*2 *\/ 23 *sin|--| 2 *\/ 3 *\/ 23 *sin|--| I*2 *\/ 3 *\/ 23 *cos|--|| | 2 *\/ 23 *cos|--|*cos|----| 2 *\/ 23 *sin|--|*sin|----| I*2 *\/ 23 *cos|--|*sin|----| I*2 *\/ 23 *cos|----|*sin|--|| | 2 *\/ 23 *cos|--|*cos|----| 2 *\/ 23 *sin|--|*sin|----| I*2 *\/ 23 *cos|----|*sin|--| I*2 *\/ 23 *cos|--|*sin|----|| | 2 *\/ 23 *cos|--|*cos|----| 2 *\/ 23 *sin|--|*sin|----| I*2 *\/ 23 *cos|--|*sin|----| I*2 *\/ 23 *cos|----|*sin|--|| | 2 *\/ 23 *cos|--|*cos|----| 2 *\/ 23 *sin|--|*sin|----| I*2 *\/ 23 *cos|----|*sin|--| I*2 *\/ 23 *cos|--|*sin|----|| | 2 *\/ 23 *cos|--|*cos|----| 2 *\/ 23 *sin|--|*sin|----| I*2 *\/ 23 *cos|--|*sin|----| I*2 *\/ 23 *cos|----|*sin|--|| | 2 *\/ 23 *cos|--|*cos|----| 2 *\/ 23 *sin|--|*sin|----| I*2 *\/ 23 *cos|----|*sin|--| I*2 *\/ 23 *cos|--|*sin|----|| | 2 *\/ 23 *cos|--|*cos|----| 2 *\/ 23 *sin|--|*sin|----| I*2 *\/ 23 *cos|--|*sin|----| I*2 *\/ 23 *cos|----|*sin|--|| | 2 *\/ 23 *cos|--|*cos|----| 2 *\/ 23 *sin|--|*sin|----| I*2 *\/ 23 *cos|----|*sin|--| I*2 *\/ 23 *cos|--|*sin|----|| | 2 *\/ 23 *cos|--|*cos|-----| 2 *\/ 23 *sin|--|*sin|-----| I*2 *\/ 23 *cos|--|*sin|-----| I*2 *\/ 23 *cos|-----|*sin|--|| | 2 *\/ 23 *cos|--|*cos|--| 2 *\/ 23 *sin|--|*sin|--| I*2 *\/ 23 *cos|--|*sin|--| I*2 *\/ 23 *cos|--|*sin|--|| | 2 *\/ 23 *sin|--|*sin|--| 2 *\/ 23 *cos|--|*cos|--| I*2 *\/ 23 *cos|--|*sin|--| I*2 *\/ 23 *cos|--|*sin|--|| | 2 *\/ 23 *cos|--|*cos|----| 2 *\/ 23 *sin|--|*sin|----| I*2 *\/ 23 *cos|--|*sin|----| I*2 *\/ 23 *cos|----|*sin|--|| | 2 *\/ 23 *sin|--|*sin|----| 2 *\/ 23 *cos|--|*cos|----| I*2 *\/ 23 *cos|--|*sin|----| I*2 *\/ 23 *cos|----|*sin|--|| | 2 *\/ 23 *cos|--|*cos|----| 2 *\/ 23 *sin|--|*sin|----| I*2 *\/ 23 *cos|--|*sin|----| I*2 *\/ 23 *cos|----|*sin|--|| | 2 *\/ 23 *sin|--|*sin|----| 2 *\/ 23 *cos|--|*cos|----| I*2 *\/ 23 *cos|--|*sin|----| I*2 *\/ 23 *cos|----|*sin|--|| | 2 *\/ 23 *cos|--|*cos|-----| 2 *\/ 23 *sin|--|*sin|-----| I*2 *\/ 23 *cos|-----|*sin|--| I*2 *\/ 23 *cos|--|*sin|-----|| | \21/ \21/| | \21/ \21/| | \21/ \21/ 21 21____ /pi\ /pi\| | \21/ \21/ \21/ \21/| | \21/ \21/ \21/ \21/| | \21/ \ 21 / \21/ \ 21 / \21/ \ 21 / \ 21 / \21/| | \21/ \ 21 / \21/ \ 21 / \ 21 / \21/ \21/ \ 21 /| | \21/ \ 21 / \21/ \ 21 / \21/ \ 21 / \ 21 / \21/| | \21/ \ 21 / \21/ \ 21 / \ 21 / \21/ \21/ \ 21 /| | \21/ \ 7 / \21/ \ 7 / \21/ \ 7 / \ 7 / \21/| | \21/ \ 7 / \21/ \ 7 / \ 7 / \21/ \21/ \ 7 /| | \21/ \ 21 / \21/ \ 21 / \21/ \ 21 / \ 21 / \21/| | \21/ \ 21 / \21/ \ 21 / \ 21 / \21/ \21/ \ 21 /| | \21/ \ 21 / \21/ \ 21 / \21/ \ 21 / \ 21 / \21/| | \7 / \21/ \7 / \21/ \21/ \7 / \7 / \21/| | \7 / \21/ \7 / \21/ \7 / \21/ \21/ \7 /| | \21/ \ 21 / \21/ \ 21 / \21/ \ 21 / \ 21 / \21/| | \21/ \ 21 / \21/ \ 21 / \21/ \ 21 / \ 21 / \21/| | \21/ \ 7 / \21/ \ 7 / \21/ \ 7 / \ 7 / \21/| | \21/ \ 7 / \21/ \ 7 / \21/ \ 7 / \ 7 / \21/| | \21/ \ 21 / \21/ \ 21 / \ 21 / \21/ \21/ \ 21 /| x*|x + - ------------------ - --------------------|*|x + ------------------- + -------------------|*|x + - ------------------- + ------------------- + I*2 *\/ 23 *cos|--|*sin|--||*|x + ------------------ + -------------------- + ------------------------ - --------------------------|*|x + ------------------ + -------------------- - ------------------------ + --------------------------|*|x + - ---------------------------- + ---------------------------- - ------------------------------ - ------------------------------|*|x + - ---------------------------- - 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/ \ 2 2 \21/ \21// \ 4 4 4 4 / \ 4 4 4 4 / \ 2 2 2 2 / \ 2 2 2 2 / \ 2 2 2 2 / \ 2 2 2 2 / \ 2 2 2 2 / \ 2 2 2 2 / \ 2 2 2 2 / \ 2 2 2 2 / \ 2 2 2 2 / \ 2 2 2 2 / \ 2 2 2 2 / \ 2 2 2 2 / \ 2 2 2 2 / \ 2 2 2 2 / \ 2 2 2 2 / \ 2 2 2 2 /
$$x \left(x + \left(- \frac{2^{\frac{20}{21}} \sqrt[21]{23} \cos{\left(\frac{\pi}{21} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{\pi}{21} \right)}}{2}\right)\right) \left(x + \left(\frac{2^{\frac{20}{21}} \sqrt[21]{23} \sin^{2}{\left(\frac{\pi}{21} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} \cos^{2}{\left(\frac{\pi}{21} \right)}}{2}\right)\right) \left(x + \left(- \frac{2^{\frac{20}{21}} \sqrt[21]{23} \sin^{2}{\left(\frac{\pi}{21} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} \cos^{2}{\left(\frac{\pi}{21} \right)}}{2} + 2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{\pi}{21} \right)}\right)\right) \left(x + \left(\frac{2^{\frac{20}{21}} \sqrt[21]{23} \sqrt{3} \sin{\left(\frac{\pi}{21} \right)}}{4} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} \cos{\left(\frac{\pi}{21} \right)}}{4} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} \sqrt{3} i \cos{\left(\frac{\pi}{21} \right)}}{4} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{\pi}{21} \right)}}{4}\right)\right) \left(x + \left(- \frac{2^{\frac{20}{21}} \sqrt[21]{23} \sqrt{3} \sin{\left(\frac{\pi}{21} \right)}}{4} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} \cos{\left(\frac{\pi}{21} \right)}}{4} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{\pi}{21} \right)}}{4} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} \sqrt{3} i \cos{\left(\frac{\pi}{21} \right)}}{4}\right)\right) \left(x + \left(- \frac{2^{\frac{20}{21}} \sqrt[21]{23} \cos{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{2 \pi}{21} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} \sin{\left(\frac{\pi}{21} \right)} \sin{\left(\frac{2 \pi}{21} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{2 \pi}{21} \right)} \cos{\left(\frac{\pi}{21} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{2 \pi}{21} \right)}}{2}\right)\right) \left(x + \left(- \frac{2^{\frac{20}{21}} \sqrt[21]{23} \cos{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{2 \pi}{21} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} \sin{\left(\frac{\pi}{21} \right)} \sin{\left(\frac{2 \pi}{21} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{2 \pi}{21} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{2 \pi}{21} \right)} \cos{\left(\frac{\pi}{21} \right)}}{2}\right)\right) \left(x + \left(- \frac{2^{\frac{20}{21}} \sqrt[21]{23} \cos{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{4 \pi}{21} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} \sin{\left(\frac{\pi}{21} \right)} \sin{\left(\frac{4 \pi}{21} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{4 \pi}{21} \right)} \cos{\left(\frac{\pi}{21} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{4 \pi}{21} \right)}}{2}\right)\right) \left(x + \left(- \frac{2^{\frac{20}{21}} \sqrt[21]{23} \cos{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{4 \pi}{21} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} \sin{\left(\frac{\pi}{21} \right)} \sin{\left(\frac{4 \pi}{21} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{4 \pi}{21} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{4 \pi}{21} \right)} \cos{\left(\frac{\pi}{21} \right)}}{2}\right)\right) \left(x + \left(- \frac{2^{\frac{20}{21}} \sqrt[21]{23} \cos{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{2 \pi}{7} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} \sin{\left(\frac{\pi}{21} \right)} \sin{\left(\frac{2 \pi}{7} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{2 \pi}{7} \right)} \cos{\left(\frac{\pi}{21} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{2 \pi}{7} \right)}}{2}\right)\right) \left(x + \left(- \frac{2^{\frac{20}{21}} \sqrt[21]{23} \cos{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{2 \pi}{7} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} \sin{\left(\frac{\pi}{21} \right)} \sin{\left(\frac{2 \pi}{7} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{2 \pi}{7} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{2 \pi}{7} \right)} \cos{\left(\frac{\pi}{21} \right)}}{2}\right)\right) \left(x + \left(- \frac{2^{\frac{20}{21}} \sqrt[21]{23} \cos{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{8 \pi}{21} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} \sin{\left(\frac{\pi}{21} \right)} \sin{\left(\frac{8 \pi}{21} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{8 \pi}{21} \right)} \cos{\left(\frac{\pi}{21} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{8 \pi}{21} \right)}}{2}\right)\right) \left(x + \left(- \frac{2^{\frac{20}{21}} \sqrt[21]{23} \cos{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{8 \pi}{21} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} \sin{\left(\frac{\pi}{21} \right)} \sin{\left(\frac{8 \pi}{21} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{8 \pi}{21} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{8 \pi}{21} \right)} \cos{\left(\frac{\pi}{21} \right)}}{2}\right)\right) \left(x + \left(- \frac{2^{\frac{20}{21}} \sqrt[21]{23} \cos{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{10 \pi}{21} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} \sin{\left(\frac{\pi}{21} \right)} \sin{\left(\frac{10 \pi}{21} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{10 \pi}{21} \right)} \cos{\left(\frac{\pi}{21} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{10 \pi}{21} \right)}}{2}\right)\right) \left(x + \left(\frac{2^{\frac{20}{21}} \sqrt[21]{23} \sin{\left(\frac{\pi}{21} \right)} \sin{\left(\frac{\pi}{7} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} \cos{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{\pi}{7} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{\pi}{21} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{\pi}{7} \right)}}{2}\right)\right) \left(x + \left(- \frac{2^{\frac{20}{21}} \sqrt[21]{23} \sin{\left(\frac{\pi}{21} \right)} \sin{\left(\frac{\pi}{7} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} \cos{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{\pi}{7} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{\pi}{7} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{\pi}{7} \right)} \cos{\left(\frac{\pi}{21} \right)}}{2}\right)\right) \left(x + \left(\frac{2^{\frac{20}{21}} \sqrt[21]{23} \sin{\left(\frac{\pi}{21} \right)} \sin{\left(\frac{5 \pi}{21} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} \cos{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{5 \pi}{21} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{5 \pi}{21} \right)} \cos{\left(\frac{\pi}{21} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{5 \pi}{21} \right)}}{2}\right)\right) \left(x + \left(- \frac{2^{\frac{20}{21}} \sqrt[21]{23} \sin{\left(\frac{\pi}{21} \right)} \sin{\left(\frac{5 \pi}{21} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} \cos{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{5 \pi}{21} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{5 \pi}{21} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{5 \pi}{21} \right)} \cos{\left(\frac{\pi}{21} \right)}}{2}\right)\right) \left(x + \left(\frac{2^{\frac{20}{21}} \sqrt[21]{23} \sin{\left(\frac{\pi}{21} \right)} \sin{\left(\frac{3 \pi}{7} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} \cos{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{3 \pi}{7} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{3 \pi}{7} \right)} \cos{\left(\frac{\pi}{21} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{3 \pi}{7} \right)}}{2}\right)\right) \left(x + \left(- \frac{2^{\frac{20}{21}} \sqrt[21]{23} \sin{\left(\frac{\pi}{21} \right)} \sin{\left(\frac{3 \pi}{7} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} \cos{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{3 \pi}{7} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{3 \pi}{7} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{3 \pi}{7} \right)} \cos{\left(\frac{\pi}{21} \right)}}{2}\right)\right) \left(x + \left(- \frac{2^{\frac{20}{21}} \sqrt[21]{23} \sin{\left(\frac{\pi}{21} \right)} \sin{\left(\frac{10 \pi}{21} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} \cos{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{10 \pi}{21} \right)}}{2} - \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{\pi}{21} \right)} \cos{\left(\frac{10 \pi}{21} \right)}}{2} + \frac{2^{\frac{20}{21}} \sqrt[21]{23} i \sin{\left(\frac{10 \pi}{21} \right)} \cos{\left(\frac{\pi}{21} \right)}}{2}\right)\right)$$
((((((((((((((((((((x*(x - 2^(20/21)*23^(1/21)*cos(pi/21)/2 - i*2^(20/21)*23^(1/21)*sin(pi/21)/2))*(x + 2^(20/21)*23^(1/21)*cos(pi/21)^2/2 + 2^(20/21)*23^(1/21)*sin(pi/21)^2/2))*(x - 2^(20/21)*23^(1/21)*sin(pi/21)^2/2 + 2^(20/21)*23^(1/21)*cos(pi/21)^2/2 + i*2^(20/21)*23^(1/21)*cos(pi/21)*sin(pi/21)))*(x + 2^(20/21)*23^(1/21)*cos(pi/21)/4 + i*2^(20/21)*23^(1/21)*sin(pi/21)/4 + 2^(20/21)*sqrt(3)*23^(1/21)*sin(pi/21)/4 - i*2^(20/21)*sqrt(3)*23^(1/21)*cos(pi/21)/4))*(x + 2^(20/21)*23^(1/21)*cos(pi/21)/4 + i*2^(20/21)*23^(1/21)*sin(pi/21)/4 - 2^(20/21)*sqrt(3)*23^(1/21)*sin(pi/21)/4 + i*2^(20/21)*sqrt(3)*23^(1/21)*cos(pi/21)/4))*(x - 2^(20/21)*23^(1/21)*cos(pi/21)*cos(2*pi/21)/2 + 2^(20/21)*23^(1/21)*sin(pi/21)*sin(2*pi/21)/2 - i*2^(20/21)*23^(1/21)*cos(pi/21)*sin(2*pi/21)/2 - i*2^(20/21)*23^(1/21)*cos(2*pi/21)*sin(pi/21)/2))*(x - 2^(20/21)*23^(1/21)*cos(pi/21)*cos(2*pi/21)/2 - 2^(20/21)*23^(1/21)*sin(pi/21)*sin(2*pi/21)/2 - i*2^(20/21)*23^(1/21)*cos(2*pi/21)*sin(pi/21)/2 + i*2^(20/21)*23^(1/21)*cos(pi/21)*sin(2*pi/21)/2))*(x - 2^(20/21)*23^(1/21)*cos(pi/21)*cos(4*pi/21)/2 + 2^(20/21)*23^(1/21)*sin(pi/21)*sin(4*pi/21)/2 - i*2^(20/21)*23^(1/21)*cos(pi/21)*sin(4*pi/21)/2 - i*2^(20/21)*23^(1/21)*cos(4*pi/21)*sin(pi/21)/2))*(x - 2^(20/21)*23^(1/21)*cos(pi/21)*cos(4*pi/21)/2 - 2^(20/21)*23^(1/21)*sin(pi/21)*sin(4*pi/21)/2 - i*2^(20/21)*23^(1/21)*cos(4*pi/21)*sin(pi/21)/2 + i*2^(20/21)*23^(1/21)*cos(pi/21)*sin(4*pi/21)/2))*(x - 2^(20/21)*23^(1/21)*cos(pi/21)*cos(2*pi/7)/2 + 2^(20/21)*23^(1/21)*sin(pi/21)*sin(2*pi/7)/2 - i*2^(20/21)*23^(1/21)*cos(pi/21)*sin(2*pi/7)/2 - i*2^(20/21)*23^(1/21)*cos(2*pi/7)*sin(pi/21)/2))*(x - 2^(20/21)*23^(1/21)*cos(pi/21)*cos(2*pi/7)/2 - 2^(20/21)*23^(1/21)*sin(pi/21)*sin(2*pi/7)/2 - i*2^(20/21)*23^(1/21)*cos(2*pi/7)*sin(pi/21)/2 + i*2^(20/21)*23^(1/21)*cos(pi/21)*sin(2*pi/7)/2))*(x - 2^(20/21)*23^(1/21)*cos(pi/21)*cos(8*pi/21)/2 + 2^(20/21)*23^(1/21)*sin(pi/21)*sin(8*pi/21)/2 - i*2^(20/21)*23^(1/21)*cos(pi/21)*sin(8*pi/21)/2 - i*2^(20/21)*23^(1/21)*cos(8*pi/21)*sin(pi/21)/2))*(x - 2^(20/21)*23^(1/21)*cos(pi/21)*cos(8*pi/21)/2 - 2^(20/21)*23^(1/21)*sin(pi/21)*sin(8*pi/21)/2 - i*2^(20/21)*23^(1/21)*cos(8*pi/21)*sin(pi/21)/2 + i*2^(20/21)*23^(1/21)*cos(pi/21)*sin(8*pi/21)/2))*(x - 2^(20/21)*23^(1/21)*cos(pi/21)*cos(10*pi/21)/2 + 2^(20/21)*23^(1/21)*sin(pi/21)*sin(10*pi/21)/2 - i*2^(20/21)*23^(1/21)*cos(pi/21)*sin(10*pi/21)/2 - i*2^(20/21)*23^(1/21)*cos(10*pi/21)*sin(pi/21)/2))*(x + 2^(20/21)*23^(1/21)*cos(pi/7)*cos(pi/21)/2 + 2^(20/21)*23^(1/21)*sin(pi/7)*sin(pi/21)/2 - i*2^(20/21)*23^(1/21)*cos(pi/21)*sin(pi/7)/2 + i*2^(20/21)*23^(1/21)*cos(pi/7)*sin(pi/21)/2))*(x - 2^(20/21)*23^(1/21)*sin(pi/7)*sin(pi/21)/2 + 2^(20/21)*23^(1/21)*cos(pi/7)*cos(pi/21)/2 + i*2^(20/21)*23^(1/21)*cos(pi/7)*sin(pi/21)/2 + i*2^(20/21)*23^(1/21)*cos(pi/21)*sin(pi/7)/2))*(x + 2^(20/21)*23^(1/21)*cos(pi/21)*cos(5*pi/21)/2 + 2^(20/21)*23^(1/21)*sin(pi/21)*sin(5*pi/21)/2 - i*2^(20/21)*23^(1/21)*cos(pi/21)*sin(5*pi/21)/2 + i*2^(20/21)*23^(1/21)*cos(5*pi/21)*sin(pi/21)/2))*(x - 2^(20/21)*23^(1/21)*sin(pi/21)*sin(5*pi/21)/2 + 2^(20/21)*23^(1/21)*cos(pi/21)*cos(5*pi/21)/2 + i*2^(20/21)*23^(1/21)*cos(pi/21)*sin(5*pi/21)/2 + i*2^(20/21)*23^(1/21)*cos(5*pi/21)*sin(pi/21)/2))*(x + 2^(20/21)*23^(1/21)*cos(pi/21)*cos(3*pi/7)/2 + 2^(20/21)*23^(1/21)*sin(pi/21)*sin(3*pi/7)/2 - i*2^(20/21)*23^(1/21)*cos(pi/21)*sin(3*pi/7)/2 + i*2^(20/21)*23^(1/21)*cos(3*pi/7)*sin(pi/21)/2))*(x - 2^(20/21)*23^(1/21)*sin(pi/21)*sin(3*pi/7)/2 + 2^(20/21)*23^(1/21)*cos(pi/21)*cos(3*pi/7)/2 + i*2^(20/21)*23^(1/21)*cos(pi/21)*sin(3*pi/7)/2 + i*2^(20/21)*23^(1/21)*cos(3*pi/7)*sin(pi/21)/2))*(x - 2^(20/21)*23^(1/21)*cos(pi/21)*cos(10*pi/21)/2 - 2^(20/21)*23^(1/21)*sin(pi/21)*sin(10*pi/21)/2 - i*2^(20/21)*23^(1/21)*cos(10*pi/21)*sin(pi/21)/2 + i*2^(20/21)*23^(1/21)*cos(pi/21)*sin(10*pi/21)/2)
Combining rational expressions
[src]
2 / 21\
y *\23 + 2*y /
---------------
46
$$\frac{y^{2} \left(2 y^{21} + 23\right)}{46}$$
y^2*(23 + 2*y^21)/46
Rational denominator
[src]
23 2
2*y + 23*y
-------------
46
$$\frac{2 y^{23} + 23 y^{2}}{46}$$
(2*y^23 + 23*y^2)/46
Combinatorics
[src]
2 / 21\
y *\23 + 2*y /
---------------
46
$$\frac{y^{2} \left(2 y^{21} + 23\right)}{46}$$
y^2*(23 + 2*y^21)/46