\(x^9-x^7+x^6-x^5-x^4+x^3-x^2+1\)
\(=\left(x^9-x^7\right)+\left(x^6-x^5\right)-\left(x^4-x^3\right)-\left(x^2-1\right)\)
\(=x^7\left(x^2-1\right)+x^5\left(x-1\right)-x^3\left(x-1\right)-\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(x^7-1\right)+\left(x-1\right)\left(x^5-x^3\right)\)
\(=\left(x^2-1\right)\left(x^7-1\right)+x^3\left(x-1\right)\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left[x^7-1+x^3\left(x-1\right)\right]\)
\(=\left(x+1\right)\left(x-1\right)\left(x^7+x^4-x^3-1\right)\)
\(=\left(x+1\right)\left(x-1\right)\left[x^4\left(x^3+1\right)-\left(x^3+1\right)\right]\)
\(=\left(x+1\right)\left(x-1\right)\left(x^3+1\right)\left(x^4-1\right)\)
\(=\left(x+1\right)^3\left(x-1\right)^2\left(x^2+1\right)\left(x^2-x+1\right)\)
Tham khảo nhé~
