a) \(x^3-4x^2+5x-2=\left(x^3-x^2\right)-\left(3x^2-3x\right)+\left(2x-2\right)=\left(x-1\right)\left(x^2-3x+2\right)=\left(x-1\right)\left(\left(x^2-x\right)-\left(2x-2\right)\right)=\left(x-2\right)\left(x-1\right)^2\)
b) \(x^5+x+1=x^5-x^2+x^2+x+1=x^2\left(x^3-1\right)+\left(x^2+x+1\right)=x^2\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)=\left(x^2+x+1\right)\left(x^3-x^2+1\right)\)
c) \(x^3+5x^2+5x+1=\left(x+1\right)\left(x^2-x+1\right)+5x\left(x+1\right)=\left(x+1\right)\left(x^2+4x+1\right)\)
