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Expression simplification/ Factorization polynomials/ x^4-2*x-6*x^2+5*x+2

Factor polynomial x^4-2*x-6*x^2+5*x+2

An expression to simplify:

The solution

You have entered [src] 
 4            2          
x  - 2*x - 6*x  + 5*x + 2
$$\left(5 x + \left(- 6 x^{2} + \left(x^{4} - 2 x\right)\right)\right) + 2$$ 
x^4 - 2*x - 6*x^2 + 5*x + 2
General simplification [src] 
     4      2      
2 + x  - 6*x  + 3*x
$$x^{4} - 6 x^{2} + 3 x + 2$$ 
2 + x^4 - 6*x^2 + 3*x
Factorization [src] 
                /          ___\ /          ___\
                |    3   \/ 5 | |    3   \/ 5 |
(x - 1)*(x - 2)*|x + - + -----|*|x + - - -----|
                \    2     2  / \    2     2  /
$$\left(x - 2\right) \left(x - 1\right) \left(x + \left(\frac{\sqrt{5}}{2} + \frac{3}{2}\right)\right) \left(x + \left(\frac{3}{2} - \frac{\sqrt{5}}{2}\right)\right)$$ 
(((x - 1)*(x - 2))*(x + 3/2 + sqrt(5)/2))*(x + 3/2 - sqrt(5)/2)
Common denominator [src] 
     4      2      
2 + x  - 6*x  + 3*x
$$x^{4} - 6 x^{2} + 3 x + 2$$ 
2 + x^4 - 6*x^2 + 3*x
Trigonometric part [src] 
     4      2      
2 + x  - 6*x  + 3*x
$$x^{4} - 6 x^{2} + 3 x + 2$$ 
2 + x^4 - 6*x^2 + 3*x
Numerical answer [src] 
2.0 + x^4 + 3.0*x - 6.0*x^2
2.0 + x^4 + 3.0*x - 6.0*x^2
Combinatorics [src] 
                  /     2      \
(-1 + x)*(-2 + x)*\1 + x  + 3*x/
$$\left(x - 2\right) \left(x - 1\right) \left(x^{2} + 3 x + 1\right)$$ 
(-1 + x)*(-2 + x)*(1 + x^2 + 3*x)
Combining rational expressions [src] 
      /     3      \
2 + x*\3 + x  - 6*x/
$$x \left(x^{3} - 6 x + 3\right) + 2$$ 
2 + x*(3 + x^3 - 6*x)
Rational denominator [src] 
     4      2      
2 + x  - 6*x  + 3*x
$$x^{4} - 6 x^{2} + 3 x + 2$$ 
2 + x^4 - 6*x^2 + 3*x
Assemble expression [src] 
     4      2      
2 + x  - 6*x  + 3*x
$$x^{4} - 6 x^{2} + 3 x + 2$$ 
2 + x^4 - 6*x^2 + 3*x
Powers [src] 
     4      2      
2 + x  - 6*x  + 3*x
$$x^{4} - 6 x^{2} + 3 x + 2$$ 
2 + x^4 - 6*x^2 + 3*x
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