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For example,

P=7*x^3+2*x^4+2

you can extract its coefficients as follows:

P.coefficients()

to get

[[2, 0], [7, 3], [2, 4]]

So the last sublist contains the answer, in this case 2 is the coefficient of x^4.

To extract this automatically you can define a function that takes a polynomial as argument:

def get_highest_coeff(P):
    m = P.coefficients()
    ncoeffs = len(m)
    return m[ncoeffs - 1][0]

And use it like this:

get_highest_coeff(P)

to get 2 as the answer. Hope this helps you get going!