a/ \(x^3-x^2-4=x^3-2x^2+x^2-4=x^2\left(x-2\right)+\left(x-2\right)\left(x+2\right)=\left(x-2\right)\left(x^2+x+2\right)\)

b/ \(x^3+5x^2+8x+4=x^3+4x^2+4x+x^2+4x+4=x\left(x^2+4x+4\right)+\left(x^2+4x+4\right)=x\left(x+2\right)^2+\left(x+2\right)^2=\left(x+2\right)^2\left(x+1\right)\)

c/ Phân tích đa thức thành nhân tử

d/ Phân tích đa thức

e/ \(x^4+6x^3+7x^2-6x+1=x^4-2x^2+1+6x^3-6x+9x^2=\left(x^2-1\right)^2+6x\left(x^2-1\right)+9x^2=\left(x^2-1+3x\right)^2=\left(x^2+3x-1\right)^2\)

f/ \(2x^4-3x^3-7x^2+6x+8=\left(2x^4-4x^3\right)+\left(x^3-2x^2\right)-\left(5x^2-10x\right)-\left(4x-8\right)=2x^3\left(x-2\right)+x^2\left(x-2\right)-5x\left(x-2\right)-4\left(x-2\right)=\left(x-2\right)\left(2x^3+x^2-5x-4\right)=\left(x-2\right)\left[\left(2x^3+2x^2\right)-\left(x^2+x\right)-\left(4x+4\right)\right]=\left(x-2\right)\left[2x^2\left(x+1\right)-x\left(x+1\right)-4\left(x+1\right)\right]=\left(x-2\right)\left(x+1\right)\left(2x^2-x-4\right)\)