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