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Expression simplification/ Factorization polynomials/ x^10-1

Factor polynomial x^10-1

An expression to simplify:

The solution

You have entered [src] 
 10    
x   - 1
$$x^{10} - 1$$ 
x^10 - 1
Factorization [src] 
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(x + 1)*(x - 1)*|x + - - ----- + I*  /   - + ----- |*|x + - - ----- - I*  /   - + ----- |*|x + - - - ----- + I*  /   - - ----- |*|x + - - - ----- - I*  /   - - ----- |*|x + - + ----- + I*  /   - - ----- |*|x + - + ----- - I*  /   - - ----- |*|x + - - + ----- + I*  /   - + ----- |*|x + - - + ----- - I*  /   - + ----- |
                \    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   /
$$\left(x - 1\right) \left(x + 1\right) \left(x + \left(- \frac{\sqrt{5}}{4} + \frac{1}{4} + i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(x + \left(- \frac{\sqrt{5}}{4} + \frac{1}{4} - i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(x + \left(- \frac{\sqrt{5}}{4} - \frac{1}{4} + i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(x + \left(- \frac{\sqrt{5}}{4} - \frac{1}{4} - i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(x + \left(\frac{1}{4} + \frac{\sqrt{5}}{4} + i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(x + \left(\frac{1}{4} + \frac{\sqrt{5}}{4} - i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(x + \left(- \frac{1}{4} + \frac{\sqrt{5}}{4} + i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(x + \left(- \frac{1}{4} + \frac{\sqrt{5}}{4} - i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right)$$ 
(((((((((x + 1)*(x - 1))*(x + 1/4 - sqrt(5)/4 + i*sqrt(5/8 + sqrt(5)/8)))*(x + 1/4 - sqrt(5)/4 - i*sqrt(5/8 + sqrt(5)/8)))*(x - 1/4 - sqrt(5)/4 + i*sqrt(5/8 - sqrt(5)/8)))*(x - 1/4 - sqrt(5)/4 - i*sqrt(5/8 - sqrt(5)/8)))*(x + 1/4 + sqrt(5)/4 + i*sqrt(5/8 - sqrt(5)/8)))*(x + 1/4 + sqrt(5)/4 - i*sqrt(5/8 - sqrt(5)/8)))*(x - 1/4 + sqrt(5)/4 + i*sqrt(5/8 + sqrt(5)/8)))*(x - 1/4 + sqrt(5)/4 - i*sqrt(5/8 + sqrt(5)/8))
Combinatorics [src] 
                 /         2    3    4\ /     2    4        3\
(1 + x)*(-1 + x)*\1 + x + x  + x  + x /*\1 + x  + x  - x - x /
$$\left(x - 1\right) \left(x + 1\right) \left(x^{4} - x^{3} + x^{2} - x + 1\right) \left(x^{4} + x^{3} + x^{2} + x + 1\right)$$ 
(1 + x)*(-1 + x)*(1 + x + x^2 + x^3 + x^4)*(1 + x^2 + x^4 - x - x^3)
Numerical answer [src] 
-1.0 + x^10
-1.0 + x^10
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