Polynomials are closed under the operation of addition. Which statement best explains the meaning of closure of polynomials under the operation of addition?

When any two polynomials are added, the result is always a polynomial with positive coefficients.

When any two polynomials are added, the result is always a polynomial.

When any two polynomials are added, the coefficients of like terms are always added.

When any two polynomials are added, the result is always a monomial or a binomial.

Question

Alana Beltran

Mathematics

21 May, 17:08

Polynomials are closed under the operation of addition. Which statement best explains the meaning of closure of polynomials under the operation of addition?

When any two polynomials are added, the result is always a polynomial with positive coefficients.

When any two polynomials are added, the result is always a polynomial.

When any two polynomials are added, the coefficients of like terms are always added.

When any two polynomials are added, the result is always a monomial or a binomial.

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Answers (1)

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Ashtyn · Answer 1

Answer: The correct answer is the second choice: "When any two polynomials are added, the result is always a polynomial."

When a set of numbers is "closed" under an operation, it means that the resulting output answer is the same type as the input.

For example, if you add 2x + 9 and 3x + 12, you get 5x + 21.

You started with 2 polynomials and you ended with a polynomial.