Question

Andrea argues that (5m−3) (2m+4)models the closure property. What reasoning could Andrea use to argue that multiplication of polynomials is closed?

The terms in the expression are rational numbers and the product is a polynomial

The exponents of the product are integers and the product is a polynomial

The coefficients of the product are integers and the product is a polynomial

The coefficients of the product are whole numbers and the product is a polynomial

The exponents of the product are whole numbers and the product is a polynomial

Answer 1

[AI-generated answer — Bot GPT 3.5]

Andrea could argue that multiplication of polynomials is closed because when multiplying two polynomials, the result is always another polynomial. In this case, the expression (5m−3) (2m+4) results in a new polynomial with coefficients that are rational numbers. Therefore, the reasoning Andrea could use is that the product of two polynomials always results in another polynomial, therefore demonstrating the closure property of multiplication of polynomials.