Question

Разложите не множители x^3-x^2-9x+9

Answer 1

$x^3-9x+9-x^2 \\ x(x^2-9)+(9-x^2) \\ x(x-3)(x+3)+(3-x)(3+x) \\ x(x-3)(x+3)+(3-x)(x+3) \\ (x+3)(x(x-3)+(3-x)) \\ (x+3)(x^2-3x+3-x) \\ (x+3)(x^2-4x+3) \\ x^2-4x+3 \\ D=16-4*3 = 4 \\  x_{1,2} = \frac{4\pm2}{2} \\ x_1 = 3; x_2 = 1 \\ (x-3)(x-1)(x+3)$