Question

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 the polynomials are closed under subtraction who is correct

Answer 1

Kate is correct. The polynomials are indeed closed under subtraction. When Charlie subtracts 2x^2 - 2x^2, the resulting expression is 0. This 0 polynomial is still a polynomial, and therefore subtraction is closed under polynomials.