Q:

Find roots of $f(x)=\left(x^2-1\right)^2\left(x^2-2x+1\right)$

I need to find the roots for the following function:
$$f(x)=\left(x^2-1\right)^2\left(x^2-2x+1\right)$$
I guess I already found one by doing this:
$$ f(x)=(x^2-1)^2(x^2-2x+1)\\
         (x^2-1)^2 = 0 | +1\\
          x^2 = 1      | √ \\
          x = 1 \\
          P₀₁(1|0)$$
But I could need some help, to find the second zero digit.

A:

You want $f(x) = 0$. 
$$(x-1)^2(x+1)^2(x-1)^2=(x-1)^4(x+1)^2= 0 $$ 
Then roots are $x_1=1$ multiplicity $4$ and $x_2=-1$ multiplicity $2$.

