Question

Phân tích đa thức thành nhân tử

\(x^5+x-1\)

Answer 1

\(x^5+x-1=x^5-x^4+x^3+x^4-x^3+x^2-x^2+x-1=x^3\left(x^2-x+1\right)+x^2\left(x^2-x+1\right)-\left(x^2-x+1\right)=\left(x^2-x+1\right)\left(x^3+x^2-1\right)\)

Answer 2

\(x^5+x-1\)

\(=x^5+x^4-x^4+x^3-x^3+x^2-x^2+x-1\)

\(=\left(x^5-x^4+x^3\right)+\left(x^4-x^3+x^2\right)-\left(x^2-x+1\right)\)

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

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

Answer 3

\(x^5+x-1=x^5-x^4+x^3+x^4-x^3+x^2-x^2+x-1=x^3\left(x^2-x+1\right)+x^2\left(x^2-x+1\right)-\left(x^2-x+1\right)=\left(x^2-x+1\right)\left(x^3+x^2-1\right)^4x\)