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what does it mean that polynomials are closed under addition? adding polynomials never results in another polynomial. if you add polynomials, the result may or may not be a polynomial. polynomials can be added, but they cannot be subtracted. the result of adding two polynomials is always a polynomial.
In mathematics, when a set is closed under an operation, performing that operation on elements of the set always results in an element of the same set. For polynomials, adding any two polynomials will yield another polynomial.
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The result of adding two polynomials is always a polynomial.