解:设x²-2x=y。则可化为(y-2)(y-9)+6=y²-11y+24=(y-3)(y-8)=(x²-2x-3)(x²-2x-8)=(x-3)(x+1)(x-4)(x+2)
(x^2-2x-2)(x^2-2x-9)+6
=(x²-2x)²-9(x²-2x)-2(x²-2x)+18+6
=(x²-2x)²-11(x²-2x)+24
=(x²-2x-3)(x²-2x-8)
=(x-3)(x+1)(x-4)(x+2)
(x^2-2x-2)(x^2-2x-9)+6
=(x²-2x)²-11(x²-2x)+18+6
=(x²-2x)²-11(x²-2x)+24
=(x²-2x-3)(x²-2x-8)
=(x-3)(x+1)(x+2)(x-4)
(x^2-2x-2)(x^2-2x-9)+6
=(x^2-2x-2)^2-7(x^2-2x-2)+6
=(x^2-2x-2-6)(x^2-2x-2-1)
=(x^2-2x-8)(x^2-2x-3)
=(x-4)(x+2)(x-3)(x+1)
(x^2-2x-2)(x^2-2x-9)+6
=4x²-2x²-18+6
=0-18+6
=-12