Given the polynomial function \( f(x) = x^4 + 2x^3 - 7x^2 - 8x + 6 \), find the remainder when \( f(x) \) is divided by \( x-2 \). Then, determine if \( x-2 \) is a factor of \( f(x) \). Let's think step by step and output the final answer within \boxed{}.
user