\(\left(x-2\right)^4-2\left(x^2-4x+4\right)^2+1\)
\(=\left(x-2\right)^4-2\left(x-2\right)^4+1\)
\(=1-\left(x-2\right)^4\)
\(=-\left[\left(x-2\right)^4-1\right]\)
\(=-\left[\left(x-2\right)^2+1\right]\left[\left(x-2\right)^2-1\right]\)
\(=-\left[\left(x-2\right)^2+1\right]\left(x-1\right)\left(x-3\right)\)