Question

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Answer 1

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) $5\cdot m -3$, $2\cdot m + 4$ Given

2) $(5\cdot m -3)+(2\cdot m +4)$ Definition of addition

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

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

5) $7\cdot m +1$ Definition of addition/Result

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