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Expression simplification/ Factorization polynomials/ x^3-x-4

Factor polynomial x^3-x-4

An expression to simplify:

The solution

You have entered [src] 
 3        
x  - x - 4
$$\left(x^{3} - x\right) - 4$$ 
x^3 - x - 4
General simplification [src] 
      3    
-4 + x  - x
$$x^{3} - x - 4$$ 
-4 + x^3 - x
Factorization [src] 
/           _____________                                                       \ /           _____________                                                       \ /           _____________                       \
|          /       _____  /          ___\                                       | |          /       _____  /          ___\                                       | |          /       _____                        |
|         /      \/ 321   |  1   I*\/ 3 |                    1                  | |         /      \/ 321   |  1   I*\/ 3 |                    1                  | |         /      \/ 321              1          |
|x + - 3 /   2 + ------- *|- - - -------| - ------------------------------------|*|x + - 3 /   2 + ------- *|- - + -------| - ------------------------------------|*|x + - 3 /   2 + -------  - --------------------|
|      \/           9     \  2      2   /          _____________                | |      \/           9     \  2      2   /          _____________                | |      \/           9              _____________|
|                                                 /       _____  /          ___\| |                                                 /       _____  /          ___\| |                                 /       _____ |
|                                                /      \/ 321   |  1   I*\/ 3 || |                                                /      \/ 321   |  1   I*\/ 3 || |                                /      \/ 321  |
|                                           3*3 /   2 + ------- *|- - - -------|| |                                           3*3 /   2 + ------- *|- - + -------|| |                           3*3 /   2 + ------- |
\                                             \/           9     \  2      2   // \                                             \/           9     \  2      2   // \                             \/           9    /
$$\left(x + \left(- \frac{1}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{\sqrt{321}}{9} + 2}} - \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{\sqrt{321}}{9} + 2}\right)\right) \left(x + \left(- \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{\sqrt{321}}{9} + 2} - \frac{1}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{\sqrt{321}}{9} + 2}}\right)\right) \left(x + \left(- \sqrt[3]{\frac{\sqrt{321}}{9} + 2} - \frac{1}{3 \sqrt[3]{\frac{\sqrt{321}}{9} + 2}}\right)\right)$$ 
((x - (2 + sqrt(321)/9)^(1/3)*(-1/2 - i*sqrt(3)/2) - 1/(3*(2 + sqrt(321)/9)^(1/3)*(-1/2 - i*sqrt(3)/2)))*(x - (2 + sqrt(321)/9)^(1/3)*(-1/2 + i*sqrt(3)/2) - 1/(3*(2 + sqrt(321)/9)^(1/3)*(-1/2 + i*sqrt(3)/2))))*(x - (2 + sqrt(321)/9)^(1/3) - 1/(3*(2 + sqrt(321)/9)^(1/3)))
Trigonometric part [src] 
      3    
-4 + x  - x
$$x^{3} - x - 4$$ 
-4 + x^3 - x
Assemble expression [src] 
      3    
-4 + x  - x
$$x^{3} - x - 4$$ 
-4 + x^3 - x
Numerical answer [src] 
-4.0 + x^3 - x
-4.0 + x^3 - x
Common denominator [src] 
      3    
-4 + x  - x
$$x^{3} - x - 4$$ 
-4 + x^3 - x
Powers [src] 
      3    
-4 + x  - x
$$x^{3} - x - 4$$ 
-4 + x^3 - x
Rational denominator [src] 
      3    
-4 + x  - x
$$x^{3} - x - 4$$ 
-4 + x^3 - x
Combinatorics [src] 
      3    
-4 + x  - x
$$x^{3} - x - 4$$ 
-4 + x^3 - x
Combining rational expressions [src] 
       /      2\
-4 + x*\-1 + x /
$$x \left(x^{2} - 1\right) - 4$$ 
-4 + x*(-1 + x^2)
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