[yarg]

It might help if you explain what is meant by F2.

As far as I can tell you're referring to the integer finite field containing the values {0, 1}.

  2 % 2 = 0
  3 % 2 = 1
  x^n % 2 = x
  2x % 2 = 0
  (2n + 1)x % 2 = x

So there are no (distinct) constants other than 0 or 1 and no multiples or exponents of x other than 1.

These facts might be obvious to someone who understands the jargon and theory of the mathematics in question, but probably need a bit more clarity when the target is the general populace.