MHB Polynomial Proof: Verification & Correction

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    Polynomial Proof
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The attached polynomial proof is generally considered correct by participants in the discussion. However, it is suggested to enhance clarity by adding a concluding statement that indicates f(x+c) is reducible, leading to a contradiction. This addition would strengthen the overall argument of the proof. Participants are encouraged to make this adjustment for improved accuracy. Overall, the proof is on the right track with minor recommendations for enhancement.
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I would like to have verification if the following attached proof is correct. If it is not correct, what can be done to make it correct? Thanks.
 

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Alexis87 said:
I would like to have verification if the following attached proof is correct. If it is not correct, what can be done to make it correct? Thanks.

Hi Alexis87,

It looks all correct to me.
For clarity I would just add a final sentence saying that therefore f(x+c) is reducible, which is a contradiction.
 
Thread 'How to define a vector field?'

Thread 'How to define a vector field?'

Hello! In one book I saw that function ##V## of 3 variables ##V_x, V_y, V_z## (vector field in 3D) can be decomposed in a Taylor series without higher-order terms (partial derivative of second power and higher) at point ##(0,0,0)## such way: I think so: higher-order terms can be neglected because partial derivative of second power and higher are equal to 0. Is this true? And how to define vector field correctly for this case? (In the book I found nothing and my attempt was wrong...
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