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Expression simplification/ Factorization polynomials/ y^5-32

Factor polynomial y^5-32

An expression to simplify:

The solution

You have entered [src] 
 5     
y  - 32
$$y^{5} - 32$$ 
y^5 - 32
Factorization [src] 
        /                         ___________\ /                         ___________\ /                         ___________\ /                         ___________\
        |          ___           /       ___ | |          ___           /       ___ | |          ___           /       ___ | |          ___           /       ___ |
        |    1   \/ 5           /  5   \/ 5  | |    1   \/ 5           /  5   \/ 5  | |    1   \/ 5           /  5   \/ 5  | |    1   \/ 5           /  5   \/ 5  |
(x - 2)*|x + - - ----- + 2*I*  /   - + ----- |*|x + - - ----- - 2*I*  /   - + ----- |*|x + - + ----- + 2*I*  /   - - ----- |*|x + - + ----- - 2*I*  /   - - ----- |
        \    2     2         \/    8     8   / \    2     2         \/    8     8   / \    2     2         \/    8     8   / \    2     2         \/    8     8   /
$$\left(x - 2\right) \left(x + \left(- \frac{\sqrt{5}}{2} + \frac{1}{2} + 2 i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(x + \left(- \frac{\sqrt{5}}{2} + \frac{1}{2} - 2 i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{5}}{2} + 2 i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{5}}{2} - 2 i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right)$$ 
((((x - 2)*(x + 1/2 - sqrt(5)/2 + 2*i*sqrt(5/8 + sqrt(5)/8)))*(x + 1/2 - sqrt(5)/2 - 2*i*sqrt(5/8 + sqrt(5)/8)))*(x + 1/2 + sqrt(5)/2 + 2*i*sqrt(5/8 - sqrt(5)/8)))*(x + 1/2 + sqrt(5)/2 - 2*i*sqrt(5/8 - sqrt(5)/8))
Numerical answer [src] 
-32.0 + y^5
-32.0 + y^5
Combinatorics [src] 
         /      4      3      2      \
(-2 + y)*\16 + y  + 2*y  + 4*y  + 8*y/
$$\left(y - 2\right) \left(y^{4} + 2 y^{3} + 4 y^{2} + 8 y + 16\right)$$ 
(-2 + y)*(16 + y^4 + 2*y^3 + 4*y^2 + 8*y)
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