Verified answer

To say that (x - a) divides f(x) means that there exists q(x) in F[x] such that

f(x) = q(x)*(x - a).

So f(a) = q(a)*(x - a) = q(a)*0 = 0.

ouch! that is tough.

I would use the division by zero proof: if F[x] can be divided, it certainly cannot be divided by 0.

that's kind of weak. maybe rearrange the equation and use the product rule.