Explain the closure property as it relates to polynomials. Give an example. (5 points)
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For a set to be closed for an operation, it means that if you do an operation with elements of the set, the answer is also an element of the set.
Here is an example to make this clearer.
The set of whole number is closed for addition.
That means if you take any two integers, and you add them, the sum is also an integer.
Here is an example of a set that is not closed for an operation.
The set of integers is not closed for division.
If you divide an integer by another integer, the quotient is not always an integer.
Now think of polynomials and the 4 operations, addition, subtraction, multiplication, division.
(a) adding two polynomials
(b) subtracting two polynomials
(a) multiplying two polynomials
(a) dividing two polynomials
For which of the four operations of polynomials above is the answer always a polynomial, or only sometimes a polynomial?