Question

Phân tích đa thức thành nhân tử

x⁶ - x⁴ - 9x³+9x²

Answer 1

\(x^6-x^4-9x^3+9x^2\)

\(=x^6-x^5+x^5-x^4-9x^2\left(x-1\right)\)

\(=x^5\left(x-1\right)+x^4\left(x-1\right)-9x^2\left(x-1\right)\)

\(=\left(x-1\right)\left(x^5+x^4-9x^2\right)\)

Answer 2

\(x^6-x^4-9x^3+9x^2\)

\(=x^4.\left(x^2-1\right)-9x^2\left(x-1\right)\)

\(=x^4.\left(x-1\right)\left(x+1\right)-9x^2\left(x-1\right)\)

\(=\left(x-1\right)\left[x^4.\left(x+1\right)-9x^2\right]\)

Answer 3

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

\(=\left(x-1\right)\left(x^5+x^4-9x^2\right)\)

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

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