Question

Phân tích đa thức x^5+x^4+1

Answer 1

\(x^5+x^4+1=\left(x^5-x^2\right)+\left(x^4+2x^2+1\right)-x^2\)

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

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

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

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