one solution of x^3-5x^2+5x-1 find other two solutions

Question

solomonzelman · Answer

$$ f(x)=x^3-5x^2+5x-1$$
find the roots
the possible roots are going to be 
1 and -1   (the +- factors of the constant)

solomonzelman · Answer

Actually -1 doesn't work, only +1 works so lets find other zeros.

now to find the other zero we would have to divide, 


                                      x^2    -    4x   +  1
              --------------------------
 x-1      I        x^3    -   5x^2   +   5x   -   1
                       x^3   -   x^2
                      ------------
                                    - 4x^2   +   5x
                                    - 4x^2   +   4x
                                   -------------
                                                         x   -  1
                                                         x   -  1
                                                        -------
                                                                   0