Ta có: \(f\left(x\right)=x^4+8x^3+23x^2+28x+12\)
=> \(f\left(x\right)=x^4+3x^3+5x^3+15x^2+8x^2+24x+4x+12\)
=> \(f\left(x\right)=x^3\left(x+3\right)+5x^2\left(x+3\right)+8x\left(x+3\right)+4\left(x+3\right)\)
=> \(f\left(x\right)=\left(x+3\right)\left(x^3+5x^2+8x+4\right)\)
=> \(f\left(x\right)=\left(x+3\right)\left(x^3+2x^2+3x^2+6x+2x+4\right)\)
=> \(f\left(x\right)=\left(x+3\right)\left[x^2\left(x+2\right)+3x\left(x+2\right)+2\left(x+2\right)\right]\)
=> \(f\left(x\right)=\left(x+3\right)\left(x+2\right)\left(x^2+3x+2\right)\)
=> \(f\left(x\right)=\left(x+2\right)\left(x+3\right)\left(x^2+2x+x+2\right)\)
=> \(f\left(x\right)=\left(x+3\right)\left(x+2\right)\left[x\left(x+2\right)+\left(x+2\right)\right]\)
=> \(f\left(x\right)=\left(x+3\right)\left(x+2\right)^2\left(x+1\right)\)
