Recall the definition of a polynomial expression. find two polynomial expressions whose quotient, when simplified, is 1/x. use that division problem to determine whether polynomials are closed under division. then describe how the other three operations—addition, subtraction, and multiplication—are different from division of polynomials.
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Step-by-step explanation:

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

Actually 1 and x both are polynomials. Therefore 1/x is already a quotient of polynomials.

Two polynomial expressions whose quotient, when simplified, is 1/x

x+1/x^2+x

Take the common of the denominator

x+1/x(x+1)

x+1 will be cancelled out by x+1

1/x

1/x is not a polynomial, so polynomials are not closed under division.

Polynomials are closed under addition, subtraction and multiplication. Addition and multiplication are associative and commutative.

There is an additive identity which is 0.

There is a multiplicative identity which is 1