**Problem :**

While doing exam revision I am having a trouble answering a following question from the book, "An Introduction to the Theory of Computation" by Sipser. Unfortunately there's no solution on this question in a book.

Explain why the below is not a legitimate Turing machine.

M = {

The input is the polynomial p over variables x1, ..., xn

- Try all the possible settings of x1, ..., xn to integer values

- Evaluate the p on all of these settings

- If any of these settings evaluates to 0, then accept; otherwise reject. }

How to solve this?