Final answer:
The closure property ensures operations on polynomials stay within the polynomial set, while the additive inverse property states each polynomial has an additive inverse resulting in 0.
Explanation:
Closure property in mathematics refers to the property that when you perform a certain operation on elements within a set, the result is also an element of that set. For polynomials, closure means that when you add, subtract, multiply, or divide two polynomials, the result is also a polynomial.
The additive inverse property of a polynomial states that for every polynomial P(x), there exists another polynomial -P(x) such that when added together, they give 0. For example, in the polynomial set, if P(x) = 2x^2 - 3x + 1, then the additive inverse is -P(x) = -2x^2 + 3x - 1.
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