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


A.) The coefficients of the sum are whole numbers and the

sum is a polynomial.


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


C.) The exponents of the sum are whole numbers and the sum is a polynomial.


D.) The exponents of the sum are integers and the sum is a polynomial.


E.) The terms in the expression are rational numbers in the sum is a polynomial.

Answer :

xero099

Answer:

A. The coefficients of the sum are whole numbers and the sum is a polynomial.

Step-by-step explanation:

The approach to demonstrate the closure property for the sum consists in defining what a polynomial is and demonstrate that the sum of two polynomials with integer coefficients is equal to a polynomial with integer coefficients. We proceed to show the proof below:

1) [tex]5\cdot m -3[/tex], [tex]2\cdot m + 4[/tex] Given

2) [tex](5\cdot m -3)+(2\cdot m +4)[/tex] Definition of addition

3) [tex](5\cdot m +2\cdot m ) +[(-3)+4][/tex] Definition of substraction/Associative and Commutative properties

4) [tex](5+2)\cdot m +1[/tex] Distributive property/Definition of substraction

5) [tex]7\cdot m +1[/tex] Definition of addition/Result

Hence, the coefficients of the sum are whole numbers and the sum is a polynomial. The correct answer is A.

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