Whole numbers are closed under addition because the sum of two whole numbers is always a whole number. Explain how the process of checking polynomial division supports the fact that polynomials are closed under multiplication and addition.

Sample If there is no remainder, then the dividend is equal to the quotient times the divisor.

The quotient and divisor are both polynomials, and their product, the dividend, is a polynomial.

If there is a remainder, then it gets added on to the product of the quotient and the divisor.

The sum of the remainder and the product of the quotient and divisor is the dividend, which is a polynomial.

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