Algebraic Curves ( on understanding this proof)

[Firepanda]

I don't 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.

 

[Mark44]

Your scanned image is too big, at 1503 x 772 pixels. Please shrink it to no larger than about 1000 x 600 or so, so that we can read the problem without having to scroll off to the right.
Thanks

 

[Firepanda]

Is that better?

 

[Mark44]

Better, yes, but could you shrink it a bit more? 800 x 400 would be about right.
Thanks!

 

[Firepanda]

800x400 now!