Question

a. Think of polynomials as a system. For each of the following operations, determinewhether the system is closed under the operation. In each case, explain why it is closedor provide an example showing that it isn't1. AdditionType your response here:2. SubtractionType your response here:3. MultiplicationType your response here:4. DivisionType your response here:

Answer 1

1. Polynomials are closed under addition because the addition of two polynomials gives always as result a new polynomial

2. Polynomials are closed under subtraction because the subtraction between two polynomials gives always as result a new polynomial

3. Polynomials are closed under multiplication because the multiplication between two polynomials gives always as result a new polynomial

4. Polynomials are not closed under division. For example:

`(x+1)/(x^2)=(x)/(x^2)+(1)/(x^2)=(1)/(x)+(1)/(x^2)`

The result is not a polynomial.