Question

Phân tích đa thức thành nhân tử:

\(x^9-x^7+x^6-x^5-x^4+x^3-x^2+1\)

Answer 1

\(x^9-x^7+x^6-x^4-x^5+x^3-x^2+1\)

\(=x^7\left(x^2-1\right)+x^4\left(x^2-1\right)-x^3\left(x^2-1\right)-\left(x^2-1\right)\)

\(=\left(x^2-1\right)\left(x^7-x^3+x^4-1\right)\)

\(=\left(x^2-1\right)\left[x^3\left(x^4-1\right)+\left(x^4-1\right)\right]\)

\(=\left(x^2-1\right)\left(x^4-1\right)\left(x^3+1\right)\)

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

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

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