Question

Phân tích đa thức thành nhân tử:  \(x^4+2009x^2+2008x+2009\)

Answer 1

\(x^4+2009x^2+2008x+2009\)

\(=\left(x^4+x^3+x^2\right)+\left(-x^3-x^2-x\right)+\left(2009x^2+2009x+2009\right)\)

\(=x^2\left(x^2+x+1\right)-x\left(x^2+x+1\right)+2009\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+2009\right)\)

Answer 2

Ta có:

\(x^4+2009x^2+2008x+2009\)

\(=\left(x^4+x^3+x^2\right)+\left(-x^3-x^2-x\right)+\left(2009x^2+2009x+2009\right)\)

\(=x^2\left(x^2+x+1\right)-x\left(x^2+x+1\right)+2009\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+2009\right)\)