Are the vectors 4−2x+8x^2, 8x−12−12x^2 and 2x−2+2x^2 linearly independent? If they aren't, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your...

Are the vectors 4−2x+8x^2, 8x−12−12x^2 and 2x−2+2x^2 linearly independent? If they aren't, find numbers, not all zero, that make the equation below true. You should be able to explain and justify your answer.

0 = ______ (4-2x+8x^2) + ______ (8x-12-12x^2) + ______ (2x-2+2x^2)