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Expression simplification/ Factorization polynomials/ x^5+32

Factor polynomial x^5+32

An expression to simplify:

The solution

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