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Expression simplification/ Factorization polynomials/ k^6+20*k^3-16

Factor polynomial k^6+20*k^3-16

An expression to simplify:

The solution

You have entered [src] 
 6       3     
k  + 20*k  - 16
$$\left(k^{6} + 20 k^{3}\right) - 16$$ 
k^6 + 20*k^3 - 16
General simplification [src] 
       6       3
-16 + k  + 20*k
$$k^{6} + 20 k^{3} - 16$$ 
-16 + k^6 + 20*k^3
Factorization [src] 
                                                   /       ________________              ________________\ /       ________________              ________________\ /         _______________              _______________\ /         _______________              _______________\
/       ________________\ /       _______________\ |    3 /           ____        ___ 3 /           ____ | |    3 /           ____        ___ 3 /           ____ | |      3 /          ____        ___ 3 /          ____ | |      3 /          ____        ___ 3 /          ____ |
|    3 /           ____ | |    3 /          ____ | |    \/  -10 + 2*\/ 29     I*\/ 3 *\/  -10 + 2*\/ 29  | |    \/  -10 + 2*\/ 29     I*\/ 3 *\/  -10 + 2*\/ 29  | |      \/  10 + 2*\/ 29     I*\/ 3 *\/  10 + 2*\/ 29  | |      \/  10 + 2*\/ 29     I*\/ 3 *\/  10 + 2*\/ 29  |
\k - \/  -10 + 2*\/ 29  /*\k + \/  10 + 2*\/ 29  /*|k + ------------------- + ---------------------------|*|k + ------------------- - ---------------------------|*|k + - ------------------ + --------------------------|*|k + - ------------------ - --------------------------|
                                                   \             2                         2             / \             2                         2             / \              2                        2             / \              2                        2             /
$$\left(k - \sqrt[3]{-10 + 2 \sqrt{29}}\right) \left(k + \sqrt[3]{10 + 2 \sqrt{29}}\right) \left(k + \left(\frac{\sqrt[3]{-10 + 2 \sqrt{29}}}{2} + \frac{\sqrt{3} i \sqrt[3]{-10 + 2 \sqrt{29}}}{2}\right)\right) \left(k + \left(\frac{\sqrt[3]{-10 + 2 \sqrt{29}}}{2} - \frac{\sqrt{3} i \sqrt[3]{-10 + 2 \sqrt{29}}}{2}\right)\right) \left(k + \left(- \frac{\sqrt[3]{10 + 2 \sqrt{29}}}{2} + \frac{\sqrt{3} i \sqrt[3]{10 + 2 \sqrt{29}}}{2}\right)\right) \left(k + \left(- \frac{\sqrt[3]{10 + 2 \sqrt{29}}}{2} - \frac{\sqrt{3} i \sqrt[3]{10 + 2 \sqrt{29}}}{2}\right)\right)$$ 
(((((k - (-10 + 2*sqrt(29))^(1/3))*(k + (10 + 2*sqrt(29))^(1/3)))*(k + (-10 + 2*sqrt(29))^(1/3)/2 + i*sqrt(3)*(-10 + 2*sqrt(29))^(1/3)/2))*(k + (-10 + 2*sqrt(29))^(1/3)/2 - i*sqrt(3)*(-10 + 2*sqrt(29))^(1/3)/2))*(k - (10 + 2*sqrt(29))^(1/3)/2 + i*sqrt(3)*(10 + 2*sqrt(29))^(1/3)/2))*(k - (10 + 2*sqrt(29))^(1/3)/2 - i*sqrt(3)*(10 + 2*sqrt(29))^(1/3)/2)
Common denominator [src] 
       6       3
-16 + k  + 20*k
$$k^{6} + 20 k^{3} - 16$$ 
-16 + k^6 + 20*k^3
Powers [src] 
       6       3
-16 + k  + 20*k
$$k^{6} + 20 k^{3} - 16$$ 
-16 + k^6 + 20*k^3
Numerical answer [src] 
-16.0 + k^6 + 20.0*k^3
-16.0 + k^6 + 20.0*k^3
Assemble expression [src] 
       6       3
-16 + k  + 20*k
$$k^{6} + 20 k^{3} - 16$$ 
-16 + k^6 + 20*k^3
Combining rational expressions [src] 
       3 /      3\
-16 + k *\20 + k /
$$k^{3} \left(k^{3} + 20\right) - 16$$ 
-16 + k^3*(20 + k^3)
Trigonometric part [src] 
       6       3
-16 + k  + 20*k
$$k^{6} + 20 k^{3} - 16$$ 
-16 + k^6 + 20*k^3
Rational denominator [src] 
       6       3
-16 + k  + 20*k
$$k^{6} + 20 k^{3} - 16$$ 
-16 + k^6 + 20*k^3
Combinatorics [src] 
       6       3
-16 + k  + 20*k
$$k^{6} + 20 k^{3} - 16$$ 
-16 + k^6 + 20*k^3
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