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Expression simplification/ Factorization polynomials/ x-x^6-2*x^3+x^4/4

Factor polynomial x-x^6-2*x^3+x^4/4

An expression to simplify:

The solution

You have entered [src] 
                 4
     6      3   x 
x - x  - 2*x  + --
                4
$$\frac{x^{4}}{4} + \left(- 2 x^{3} + \left(- x^{6} + x\right)\right)$$ 
x - x^6 - 2*x^3 + x^4/4
General simplification [src] 
                 4
     6      3   x 
x - x  - 2*x  + --
                4
$$- x^{6} + \frac{x^{4}}{4} - 2 x^{3} + x$$ 
x - x^6 - 2*x^3 + x^4/4
Fraction decomposition [src] 
x - x^6 - 2*x^3 + x^4/4
$$- x^{6} + \frac{x^{4}}{4} - 2 x^{3} + x$$ 
                 4
     6      3   x 
x - x  - 2*x  + --
                4
Factorization [src] 
  /           /   5    3      2       \\ /           /   5    3      2       \\ /           /   5    3      2       \\ /           /   5    3      2       \\ /           /   5    3      2       \\
x*\x - CRootOf\4*x  - x  + 8*x  - 4, 0//*\x - CRootOf\4*x  - x  + 8*x  - 4, 1//*\x - CRootOf\4*x  - x  + 8*x  - 4, 2//*\x - CRootOf\4*x  - x  + 8*x  - 4, 3//*\x - CRootOf\4*x  - x  + 8*x  - 4, 4//
$$x \left(x - \operatorname{CRootOf} {\left(4 x^{5} - x^{3} + 8 x^{2} - 4, 0\right)}\right) \left(x - \operatorname{CRootOf} {\left(4 x^{5} - x^{3} + 8 x^{2} - 4, 1\right)}\right) \left(x - \operatorname{CRootOf} {\left(4 x^{5} - x^{3} + 8 x^{2} - 4, 2\right)}\right) \left(x - \operatorname{CRootOf} {\left(4 x^{5} - x^{3} + 8 x^{2} - 4, 3\right)}\right) \left(x - \operatorname{CRootOf} {\left(4 x^{5} - x^{3} + 8 x^{2} - 4, 4\right)}\right)$$ 
((((x*(x - CRootOf(4*x^5 - x^3 + 8*x^2 - 4, 0)))*(x - CRootOf(4*x^5 - x^3 + 8*x^2 - 4, 1)))*(x - CRootOf(4*x^5 - x^3 + 8*x^2 - 4, 2)))*(x - CRootOf(4*x^5 - x^3 + 8*x^2 - 4, 3)))*(x - CRootOf(4*x^5 - x^3 + 8*x^2 - 4, 4))
Numerical answer [src] 
x - x^6 + 0.25*x^4 - 2.0*x^3
x - x^6 + 0.25*x^4 - 2.0*x^3
Common denominator [src] 
                 4
     6      3   x 
x - x  - 2*x  + --
                4
$$- x^{6} + \frac{x^{4}}{4} - 2 x^{3} + x$$ 
x - x^6 - 2*x^3 + x^4/4
Combining rational expressions [src] 
  /     3      2      5\
x*\4 + x  - 8*x  - 4*x /
------------------------
           4
$$\frac{x \left(- 4 x^{5} + x^{3} - 8 x^{2} + 4\right)}{4}$$ 
x*(4 + x^3 - 8*x^2 - 4*x^5)/4
Trigonometric part [src] 
                 4
     6      3   x 
x - x  - 2*x  + --
                4
$$- x^{6} + \frac{x^{4}}{4} - 2 x^{3} + x$$ 
x - x^6 - 2*x^3 + x^4/4
Combinatorics [src] 
   /      3      5      2\ 
-x*\-4 - x  + 4*x  + 8*x / 
---------------------------
             4
$$- \frac{x \left(4 x^{5} - x^{3} + 8 x^{2} - 4\right)}{4}$$ 
-x*(-4 - x^3 + 4*x^5 + 8*x^2)/4
Powers [src] 
                 4
     6      3   x 
x - x  - 2*x  + --
                4
$$- x^{6} + \frac{x^{4}}{4} - 2 x^{3} + x$$ 
x - x^6 - 2*x^3 + x^4/4
Assemble expression [src] 
                 4
     6      3   x 
x - x  - 2*x  + --
                4
$$- x^{6} + \frac{x^{4}}{4} - 2 x^{3} + x$$ 
x - x^6 - 2*x^3 + x^4/4
Rational denominator [src] 
 4      3      6      
x  - 8*x  - 4*x  + 4*x
----------------------
          4
$$\frac{- 4 x^{6} + x^{4} - 8 x^{3} + 4 x}{4}$$ 
(x^4 - 8*x^3 - 4*x^6 + 4*x)/4
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