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

Question

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

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

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

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

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

Answer 1

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

Andrea could argue that since the terms in the expression (5m−3) and (2m+4) are polynomials (as they are of the form ax + b where a and b are rational numbers), and the product of two polynomials is also a polynomial, then the multiplication of polynomials is closed under the operation.