Which of the following equations demonstrate the set of polynomials is not closed under the certain operations?

  see below

Step-by-step explanation:

When there as a remainder, polynomial division does not result in a polynomial. The set of polynomials is not closed for division.

The first one, i believe, would be correct. all the others have one thing in common, and that's that they have repeating numbers. in the second one, x and y have repeating 6's and 3's, and in the third, x and y have repeating 6's as well. in the last one, there are repeating 3's. the first one has no repeating numbers.