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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.
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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