Question

Phân tích đa thức sau thành nhân tử :

3(x² -x +1)^{2 -} 2x² + 2x - 3

Answer 1

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

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

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

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

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

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

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

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