Question

Phân tích các đa thức sau thành nhân tử:

\(e,x^2+y^2-x^2y^2+xy-x-y\)

\(f,x^4+2x^3-4x-4\)

Answer 1

\(e.x^2+y^2-x^2y^2+xy-x-y=x^2\left(1-y^2\right)+y\left(y-1\right)+x\left(y-1\right)=-x^2\left(y-1\right)\left(y+1\right)+y\left(y-1\right)+x\left(y-1\right)=\left(y-1\right)\left(x+y-x^2y-x^2\right)=\left(y-1\right)\left[x\left(1-x\right)+y\left(1-x\right)\left(1+x\right)\right]=\left(y-1\right)\left(1-x\right)\left(x+xy+y\right)\)

\(f.x^4+2x^3-4x-4=x^4+3x^3+x^2-x^2-4x-4=\left(x^2+x\right)^2-\left(x+2\right)^2=\left(x^2+x-x-2\right)\left(x^2+x+x+2\right)=\left(x^2-2\right)\left(x^2+2x+2\right)\)