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Factor polynomial x^6-9*x^5+34*x^4-66*x^3+64*x^2-24*x

An expression to simplify:

The solution

You have entered [src]
 6      5       4       3       2       
x  - 9*x  + 34*x  - 66*x  + 64*x  - 24*x
$$- 24 x + \left(64 x^{2} + \left(- 66 x^{3} + \left(34 x^{4} + \left(x^{6} - 9 x^{5}\right)\right)\right)\right)$$
x^6 - 9*x^5 + 34*x^4 - 66*x^3 + 64*x^2 - 24*x
Factorization [src]
                  /             ___\ /             ___\
x*(x - 1)*(x - 2)*\x + -2 + I*\/ 2 /*\x + -2 - I*\/ 2 /
$$x \left(x - 1\right) \left(x - 2\right) \left(x + \left(-2 + \sqrt{2} i\right)\right) \left(x + \left(-2 - \sqrt{2} i\right)\right)$$
(((x*(x - 1))*(x - 2))*(x - 2 + i*sqrt(2)))*(x - 2 - i*sqrt(2))
General simplification [src]
  /       5       2      4       3       \
x*\-24 + x  - 66*x  - 9*x  + 34*x  + 64*x/
$$x \left(x^{5} - 9 x^{4} + 34 x^{3} - 66 x^{2} + 64 x - 24\right)$$
x*(-24 + x^5 - 66*x^2 - 9*x^4 + 34*x^3 + 64*x)
Combinatorics [src]
          2          /     2      \
x*(-2 + x) *(-1 + x)*\6 + x  - 4*x/
$$x \left(x - 2\right)^{2} \left(x - 1\right) \left(x^{2} - 4 x + 6\right)$$
x*(-2 + x)^2*(-1 + x)*(6 + x^2 - 4*x)
Assemble expression [src]
 6       3             5       4       2
x  - 66*x  - 24*x - 9*x  + 34*x  + 64*x 
$$x^{6} - 9 x^{5} + 34 x^{4} - 66 x^{3} + 64 x^{2} - 24 x$$
x^6 - 66*x^3 - 24*x - 9*x^5 + 34*x^4 + 64*x^2
Powers [src]
 6       3             5       4       2
x  - 66*x  - 24*x - 9*x  + 34*x  + 64*x 
$$x^{6} - 9 x^{5} + 34 x^{4} - 66 x^{3} + 64 x^{2} - 24 x$$
x^6 - 66*x^3 - 24*x - 9*x^5 + 34*x^4 + 64*x^2
Combining rational expressions [src]
x*(-24 + x*(64 + x*(-66 + x*(34 + x*(-9 + x)))))
$$x \left(x \left(x \left(x \left(x \left(x - 9\right) + 34\right) - 66\right) + 64\right) - 24\right)$$
x*(-24 + x*(64 + x*(-66 + x*(34 + x*(-9 + x)))))
Numerical answer [src]
x^6 + 64.0*x^2 + 34.0*x^4 - 24.0*x - 9.0*x^5 - 66.0*x^3
x^6 + 64.0*x^2 + 34.0*x^4 - 24.0*x - 9.0*x^5 - 66.0*x^3
Common denominator [src]
 6       3             5       4       2
x  - 66*x  - 24*x - 9*x  + 34*x  + 64*x 
$$x^{6} - 9 x^{5} + 34 x^{4} - 66 x^{3} + 64 x^{2} - 24 x$$
x^6 - 66*x^3 - 24*x - 9*x^5 + 34*x^4 + 64*x^2
Trigonometric part [src]
 6       3             5       4       2
x  - 66*x  - 24*x - 9*x  + 34*x  + 64*x 
$$x^{6} - 9 x^{5} + 34 x^{4} - 66 x^{3} + 64 x^{2} - 24 x$$
x^6 - 66*x^3 - 24*x - 9*x^5 + 34*x^4 + 64*x^2
Rational denominator [src]
 6       3             5       4       2
x  - 66*x  - 24*x - 9*x  + 34*x  + 64*x 
$$x^{6} - 9 x^{5} + 34 x^{4} - 66 x^{3} + 64 x^{2} - 24 x$$
x^6 - 66*x^3 - 24*x - 9*x^5 + 34*x^4 + 64*x^2