Which is the correct degree of the taylor polynomial of this question?

Question

Ok, so for context purposes the problem is: to determine value of x for which the function can be replaced by the taylor polynomial if the error cannot exceed 0.001 My only confusion with the answer key is WHY THEY ASSUMED that this is a 5th degree taylor polynomial because technically the 4th degree taylor polynomial is the same.

Answer 1

For the purposes of the Lagrange Error Bound, they computed that a fifth degree polynomial would work. If the fifth degree polynomial and fourth degree polynomial are the same, the fourth degree polynomial works as well.