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Factor polynomial x^4-5*x^3+6*x^2-10*x+8

An expression to simplify:

The solution

You have entered [src]
 4      3      2           
x  - 5*x  + 6*x  - 10*x + 8
$$\left(- 10 x + \left(6 x^{2} + \left(x^{4} - 5 x^{3}\right)\right)\right) + 8$$
x^4 - 5*x^3 + 6*x^2 - 10*x + 8
Factorization [src]
                /        ___\ /        ___\
(x - 1)*(x - 4)*\x + I*\/ 2 /*\x - I*\/ 2 /
$$\left(x - 4\right) \left(x - 1\right) \left(x + \sqrt{2} i\right) \left(x - \sqrt{2} i\right)$$
(((x - 1)*(x - 4))*(x + i*sqrt(2)))*(x - i*sqrt(2))
General simplification [src]
     4             3      2
8 + x  - 10*x - 5*x  + 6*x 
$$x^{4} - 5 x^{3} + 6 x^{2} - 10 x + 8$$
8 + x^4 - 10*x - 5*x^3 + 6*x^2
Rational denominator [src]
     4             3      2
8 + x  - 10*x - 5*x  + 6*x 
$$x^{4} - 5 x^{3} + 6 x^{2} - 10 x + 8$$
8 + x^4 - 10*x - 5*x^3 + 6*x^2
Assemble expression [src]
     4             3      2
8 + x  - 10*x - 5*x  + 6*x 
$$x^{4} - 5 x^{3} + 6 x^{2} - 10 x + 8$$
8 + x^4 - 10*x - 5*x^3 + 6*x^2
Common denominator [src]
     4             3      2
8 + x  - 10*x - 5*x  + 6*x 
$$x^{4} - 5 x^{3} + 6 x^{2} - 10 x + 8$$
8 + x^4 - 10*x - 5*x^3 + 6*x^2
Powers [src]
     4             3      2
8 + x  - 10*x - 5*x  + 6*x 
$$x^{4} - 5 x^{3} + 6 x^{2} - 10 x + 8$$
8 + x^4 - 10*x - 5*x^3 + 6*x^2
Trigonometric part [src]
     4             3      2
8 + x  - 10*x - 5*x  + 6*x 
$$x^{4} - 5 x^{3} + 6 x^{2} - 10 x + 8$$
8 + x^4 - 10*x - 5*x^3 + 6*x^2
Combinatorics [src]
                  /     2\
(-1 + x)*(-4 + x)*\2 + x /
$$\left(x - 4\right) \left(x - 1\right) \left(x^{2} + 2\right)$$
(-1 + x)*(-4 + x)*(2 + x^2)
Numerical answer [src]
8.0 + x^4 + 6.0*x^2 - 5.0*x^3 - 10.0*x
8.0 + x^4 + 6.0*x^2 - 5.0*x^3 - 10.0*x
Combining rational expressions [src]
8 + x*(-10 + x*(6 + x*(-5 + x)))
$$x \left(x \left(x \left(x - 5\right) + 6\right) - 10\right) + 8$$
8 + x*(-10 + x*(6 + x*(-5 + x)))