Question

Phân tích đa thức thành nhân tử:

\(x^4+2008x^2+2007x+2008\)

Answer 1

Ta có:

\(x^4+2008x^2+2007x+2008\)

\(=\left(x^4+x^2+1\right)+\left(2007x^2+2007x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+1\right)+2007\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x+2008\right)\)

Answer 2

Cách này dễ hơn nè :

\(x^4+2008x^2+2007x+2008\)

= \(x^4-x+2008\left(x^2+x+1\right)\)

=\(x\left(x-1\right)\left(x^2+x+1\right)+2008\left(x^2+x+1\right)\)=\(\left(x^2+x+1\right)\left(x^2-x+2008\right)\)