Suppose that an algorithm A executes 5n3+ 20n2 + 65n + 200 steps when run with input of size n. Prove that the algorithm is in O(n3) (i.e. A is in big-O of n3).

a) Using the predicate we defined in the class for the big-O notation, translate this statement into predicate logic (that is, using predicates and quantifiers).

b) Give a proof for this statement. Your proof can be a formal proof or informal (in natural language), but it must have a similar structure of a formal proof.