Charlie subtracts two polynomials,2x^2-2x^2 , and says that the difference proves that polynomials are not closed under subtraction. Kate argues that the difference does in fact show that polynomials are closed under subtraction. Who is correct? Type only 'Charlie' or 'Kate' as your answer in the box.

  A: (3x−4)−(2x+2)=x−6

  B: The difference of the polynomials (3x−4) and (2x+2) is a polynomial, x−6, which shows closure under subtraction.

Step-by-step explanation:

Only two of the answer choices have anything to do with differences, and only one of those correctly computes the difference. That answer choice is the correct one in each case.

Often, these questions are mostly about choosing an answer that is responsive to the question. Answer choices in left-field can be ignored immediately.

When a set (polynomials) is closed under an operation (subtraction), it means that the result of that operation on any two members of the set is also a member of the set.

(Any sets containing 0 are not closed under division because division by 0 is undefined.)