Question

Phân tích đa thức thành nhân tử

X^8+x^7+1

Answer 1

Ta có :

\(x^8+x^7+1\)

\(=\left(x^8+x^7+x^6\right)-x^6+1\)

\(=x^6\left(x^2+x+1\right)-\left[\left(x^3\right)^2-1^2\right]\)

\(=x^6\left(x^2+x+1\right)-\left(x^3-1\right)\left(x^3+1\right)\)

\(=x^6\left(x^2+x+1\right)-\left(x^3+1\right)\left(x-1\right)\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left[x^6-\left(x^3+1\right)\left(x-1\right)\right]\)

\(=\left(x^2+x+1\right)\left[x^6-\left(x^4-x^3+x-1\right)\right]\)

\(=\left(x^2+x+1\right)\left(x^6-x^4+x^3-x+1\right)\)