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Expression simplification/ Factorization polynomials/ x^9+3*x^7+3*x^5+x^3-x+7

Factor polynomial x^9+3*x^7+3*x^5+x^3-x+7

An expression to simplify:

The solution

You have entered [src] 
 9      7      5    3        
x  + 3*x  + 3*x  + x  - x + 7
$$\left(- x + \left(x^{3} + \left(3 x^{5} + \left(x^{9} + 3 x^{7}\right)\right)\right)\right) + 7$$ 
x^9 + 3*x^7 + 3*x^5 + x^3 - x + 7
General simplification [src] 
     3    9          5      7
7 + x  + x  - x + 3*x  + 3*x
$$x^{9} + 3 x^{7} + 3 x^{5} + x^{3} - x + 7$$ 
7 + x^3 + x^9 - x + 3*x^5 + 3*x^7
Factorization [src] 
        /           / 8    7      6      5      4      3      2             \\ /           / 8    7      6      5      4      3      2             \\ /           / 8    7      6      5      4      3      2             \\ /           / 8    7      6      5      4      3      2             \\ /           / 8    7      6      5      4      3      2             \\ /           / 8    7      6      5      4      3      2             \\ /           / 8    7      6      5      4      3      2             \\ /           / 8    7      6      5      4      3      2             \\
(x + 1)*\x - CRootOf\x  - x  + 4*x  - 4*x  + 7*x  - 7*x  + 8*x  - 8*x + 7, 0//*\x - CRootOf\x  - x  + 4*x  - 4*x  + 7*x  - 7*x  + 8*x  - 8*x + 7, 1//*\x - CRootOf\x  - x  + 4*x  - 4*x  + 7*x  - 7*x  + 8*x  - 8*x + 7, 2//*\x - CRootOf\x  - x  + 4*x  - 4*x  + 7*x  - 7*x  + 8*x  - 8*x + 7, 3//*\x - CRootOf\x  - x  + 4*x  - 4*x  + 7*x  - 7*x  + 8*x  - 8*x + 7, 4//*\x - CRootOf\x  - x  + 4*x  - 4*x  + 7*x  - 7*x  + 8*x  - 8*x + 7, 5//*\x - CRootOf\x  - x  + 4*x  - 4*x  + 7*x  - 7*x  + 8*x  - 8*x + 7, 6//*\x - CRootOf\x  - x  + 4*x  - 4*x  + 7*x  - 7*x  + 8*x  - 8*x + 7, 7//
$$\left(x + 1\right) \left(x - \operatorname{CRootOf} {\left(x^{8} - x^{7} + 4 x^{6} - 4 x^{5} + 7 x^{4} - 7 x^{3} + 8 x^{2} - 8 x + 7, 0\right)}\right) \left(x - \operatorname{CRootOf} {\left(x^{8} - x^{7} + 4 x^{6} - 4 x^{5} + 7 x^{4} - 7 x^{3} + 8 x^{2} - 8 x + 7, 1\right)}\right) \left(x - \operatorname{CRootOf} {\left(x^{8} - x^{7} + 4 x^{6} - 4 x^{5} + 7 x^{4} - 7 x^{3} + 8 x^{2} - 8 x + 7, 2\right)}\right) \left(x - \operatorname{CRootOf} {\left(x^{8} - x^{7} + 4 x^{6} - 4 x^{5} + 7 x^{4} - 7 x^{3} + 8 x^{2} - 8 x + 7, 3\right)}\right) \left(x - \operatorname{CRootOf} {\left(x^{8} - x^{7} + 4 x^{6} - 4 x^{5} + 7 x^{4} - 7 x^{3} + 8 x^{2} - 8 x + 7, 4\right)}\right) \left(x - \operatorname{CRootOf} {\left(x^{8} - x^{7} + 4 x^{6} - 4 x^{5} + 7 x^{4} - 7 x^{3} + 8 x^{2} - 8 x + 7, 5\right)}\right) \left(x - \operatorname{CRootOf} {\left(x^{8} - x^{7} + 4 x^{6} - 4 x^{5} + 7 x^{4} - 7 x^{3} + 8 x^{2} - 8 x + 7, 6\right)}\right) \left(x - \operatorname{CRootOf} {\left(x^{8} - x^{7} + 4 x^{6} - 4 x^{5} + 7 x^{4} - 7 x^{3} + 8 x^{2} - 8 x + 7, 7\right)}\right)$$ 
((((((((x + 1)*(x - CRootOf(x^8 - x^7 + 4*x^6 - 4*x^5 + 7*x^4 - 7*x^3 + 8*x^2 - 8*x + 7, 0)))*(x - CRootOf(x^8 - x^7 + 4*x^6 - 4*x^5 + 7*x^4 - 7*x^3 + 8*x^2 - 8*x + 7, 1)))*(x - CRootOf(x^8 - x^7 + 4*x^6 - 4*x^5 + 7*x^4 - 7*x^3 + 8*x^2 - 8*x + 7, 2)))*(x - CRootOf(x^8 - x^7 + 4*x^6 - 4*x^5 + 7*x^4 - 7*x^3 + 8*x^2 - 8*x + 7, 3)))*(x - CRootOf(x^8 - x^7 + 4*x^6 - 4*x^5 + 7*x^4 - 7*x^3 + 8*x^2 - 8*x + 7, 4)))*(x - CRootOf(x^8 - x^7 + 4*x^6 - 4*x^5 + 7*x^4 - 7*x^3 + 8*x^2 - 8*x + 7, 5)))*(x - CRootOf(x^8 - x^7 + 4*x^6 - 4*x^5 + 7*x^4 - 7*x^3 + 8*x^2 - 8*x + 7, 6)))*(x - CRootOf(x^8 - x^7 + 4*x^6 - 4*x^5 + 7*x^4 - 7*x^3 + 8*x^2 - 8*x + 7, 7))
Assemble expression [src] 
     3    9          5      7
7 + x  + x  - x + 3*x  + 3*x
$$x^{9} + 3 x^{7} + 3 x^{5} + x^{3} - x + 7$$ 
7 + x^3 + x^9 - x + 3*x^5 + 3*x^7
Combining rational expressions [src] 
      /      2 /     2 /     2 /     2\\\\
7 + x*\-1 + x *\1 + x *\3 + x *\3 + x ////
$$x \left(x^{2} \left(x^{2} \left(x^{2} \left(x^{2} + 3\right) + 3\right) + 1\right) - 1\right) + 7$$ 
7 + x*(-1 + x^2*(1 + x^2*(3 + x^2*(3 + x^2))))
Rational denominator [src] 
     3    9          5      7
7 + x  + x  - x + 3*x  + 3*x
$$x^{9} + 3 x^{7} + 3 x^{5} + x^{3} - x + 7$$ 
7 + x^3 + x^9 - x + 3*x^5 + 3*x^7
Trigonometric part [src] 
     3    9          5      7
7 + x  + x  - x + 3*x  + 3*x
$$x^{9} + 3 x^{7} + 3 x^{5} + x^{3} - x + 7$$ 
7 + x^3 + x^9 - x + 3*x^5 + 3*x^7
Powers [src] 
     3    9          5      7
7 + x  + x  - x + 3*x  + 3*x
$$x^{9} + 3 x^{7} + 3 x^{5} + x^{3} - x + 7$$ 
7 + x^3 + x^9 - x + 3*x^5 + 3*x^7
Numerical answer [src] 
7.0 + x^3 + x^9 - x + 3.0*x^5 + 3.0*x^7
7.0 + x^3 + x^9 - x + 3.0*x^5 + 3.0*x^7
Combinatorics [src] 
        /     8    7            3      5      6      4      2\
(1 + x)*\7 + x  - x  - 8*x - 7*x  - 4*x  + 4*x  + 7*x  + 8*x /
$$\left(x + 1\right) \left(x^{8} - x^{7} + 4 x^{6} - 4 x^{5} + 7 x^{4} - 7 x^{3} + 8 x^{2} - 8 x + 7\right)$$ 
(1 + x)*(7 + x^8 - x^7 - 8*x - 7*x^3 - 4*x^5 + 4*x^6 + 7*x^4 + 8*x^2)
Common denominator [src] 
     3    9          5      7
7 + x  + x  - x + 3*x  + 3*x
$$x^{9} + 3 x^{7} + 3 x^{5} + x^{3} - x + 7$$ 
7 + x^3 + x^9 - x + 3*x^5 + 3*x^7
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