Question

What it means the degree of g(x) is 0?
(g(x) is a non zero element of N of minimal degree. Where N is an ideal in F[x]. )
the geometrical meaning of degree of polynomial is 0?

Answer 1

Simply degree of is means its a cosntant polynomial, means in general way it can be said that
with some constant
Detailed description is given below-

_________________
A plolynomial with degree means that it is a constant polynomial
For here we have as the polynomial with degree , it means it is a constant polynomial

To put it simple say a polynimal is given by-

Here is a polynomial with degree , if the degree is it means
, means there is no term with

So in our case we can say that is a constant polynomial, and it means the value of polynomial does not varry with change in as the constant polynomial has no term

i.e. for all value of the polynomial is constant

In generall we can say-
, where is some constant quantity
________________
So as we discussed above, the geometrical meaning of degree of polynomial is is that its value will not varry with change in , that is remains constant

So our function will be a straight line paralel to -axis
with the constant -intecept

Say we have , so its graph will have constant value i.e line parallel to -axis, with at every place