[tex]f = X^3-2X^2-2X+1 \\ \\ (x_2+x_3)(x_3+x_1)(x_1+x_2) = ? \\ \\ x_1+x_2+x_3 = -\dfrac{b}{a} = 2 \\ \\ \Rightarrow x_2+x_3 = 2-x_1 \\ \Rightarrow x_3+x_1 = 2-x_2 \\ \Rightarrow x_1+x_2 = 2-x_3 \\ \\\Rightarrow(x_2+x_3)(x_3+x_1)(x_1+x_2) = (2-x_1)(2-x_2)(2-x_3) = \\ \\ = f(2) = 2^3-2\cdot 2^2-2\cdot 2+1 = 8-8-4+1 = \boxed{-3}\\ \\ f(x) = (x-x_1)(x-x_2)(x-x_3)\\ f(2) = (2-x_1)(2-x_2)(2-x_3)[/tex]
