Ms. Adams claims that the closure properties for polynomials are closed when dividing polynomials. Mr. Aroxa claims that the closure properties for polynomials are not closed when dividing polynomials. Who is correct? Explain your answer.

Question

Kamila Jenkins

Mathematics

10 May, 14:37

Ms. Adams claims that the closure properties for polynomials are closed when dividing polynomials. Mr. Aroxa claims that the closure properties for polynomials are not closed when dividing polynomials. Who is correct? Explain your answer.

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Answers (1)

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Brendan Kemp · Answer 1

Mr. Aroxa is correct.

Step-by-step explanation:

Since we know that polynomials are closed under addition, subtraction and multiplication as when we will add, subtract or multiply two polynomials we will get a polynomial.

Polynomials are not closed under division because division of two polynomials is not necessarily a polynomial.

We can see it by dividing a binomial by a trinomial. This division will result in a rational expression and it will have negative exponent. Negative exponents are not allowed in polynomials.

Therefore, Mr. Aroxa is correct.