Question

Phân tích đa thức thành nhân tử : x⁶ - x⁴ + 2x³ + 2x²

Answer 1

\(=\left(x^6+2x^5+x^4\right)-2\left(x^5+2x^4+x^3\right)+2\left(x^4+2x^3+x^2\right)\)

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

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

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

Answer 2

\(x^6-x^4+2x^3+2x^2\)

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

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

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