Question

x³ - 6x² + 9x - 4 = ?

Answer 1

x³ - 6x² + 9x - 4

= x (x² - 6x +9) - 4

= x (x - 3)² - 4

= x (x - 7) (x + 1)

Answer 2

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

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

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

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

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

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

\(=\left(x-1\right)\left[x\left(x-1\right)-4\left(x-1\right)\right]\)

\(=\left(x-1\right)\left(x-1\right)\left(x-4\right)\)

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