How to extract the polynomial and the non-polynomial parts from a sympy equation?

You can use the as_poly method to find the terms that are polynomial in the given symbol:

In [1]: from sympy import Symbol
   ...: 
   ...: x = Symbol('x')
   ...: equation = x**2 + 2**x - 2*x - 5**x + 1

In [2]: poly, nonpoly = [], []

In [3]: for term in Add.make_args(equation):
   ...:     if term.as_poly(x) is not None:
   ...:         poly.append(term)
   ...:     else:
   ...:         nonpoly.append(term)
   ...: 

In [4]: poly
Out[4]: 
⎡    2      ⎤
⎣1, x , -2⋅x⎦

In [5]: nonpoly
Out[5]: 
⎡ x    x⎤
⎣2 , -5 ⎦

In [6]: Add(*poly)
Out[6]: 
 2          
x  - 2⋅x + 1

In [7]: Add(*nonpoly)
Out[7]: 
 x    x
2  - 5 

https://docs.sympy.org/latest/modules/core.html#sympy.core.expr.Expr.as_poly

Separate all the terms first,

lst = equation.args

Use the degree() function in sympy module to find the degree of each term in lst. It gives a PolynomialError, if a term is not a polynomial.

Error can be handled using try ... except statements.