Question

Robin says that polynomials are closed under division. Brad adamantly disagrees. Who is correct? Justify your answer.

Answer 1

Brad is correct.

Polynomials do not include negative exponents; this means there can be no variables in the denominator.  If two polynomials do not divide evenly, the remainder is written as a fraction with the divisor (which can include a variable) in the denominator.  This is not a polynomial.