Question

phân tích đa thức thành nhân tử:x^4+2002x^2-2001x+2002

Answer 1

       \(x^4+2002x^2-2001x+2002\)

\(=x^4+2002x^2+x-2002x+2002\)

\(=\left(x^4+x\right)+\left(2002x^2-2002x+2002\right)\)

\(=x\left(x^3+1\right)+2002\left(x^2-x+1\right)\)

\(=x\left(x+1\right)\left(x^2-x+1\right)+2002\left(x^2-x+1\right)\)

\(=\left(x^2-x+1\right)\left[x\left(x+1\right)+2002\right]\)

\(=\left(x^2-x+1\right)\left(x^2+x+2002\right)\)