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I dont get why G=0 is a contradiction. Does it imply F=0, which cannot be true since the question stated F is non constant?

Can anyone give me another proof for this first part please? As the step he made to get G would have been something I would never have thought of.

By the way problem 1.4 showed that if F(P) = 0 for all P then F = 0 when k is an infinite field.

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