You can prove that a statement isn't true by finding a single example that contradicts the statement, which is called a counterexample. Show that the set of polynomials is not closed under division by finding a counterexample of division of a polynomial by a polynomial that does not result in a polynomial.

allbleachix

allbleachix

Answered question

2022-09-12

You can prove that a statement isn't true by finding a single example that contradicts the statement, which is called a counterexample. Show that the set of polynomials is not closed under division by finding a counterexample of division of a polynomial by a polynomial that does not result in a polynomial.

Answer & Explanation

Gabriela Werner

Gabriela Werner

Beginner2022-09-13Added 11 answers

The expressions x and x 2 are polynomials. When the expressions are divided, the result is 1 x or x 1 . This quotient is not a polynomial since the exponent of x is a negative number. This shows that dividing two polynomials does not necessarily result to a polynomial. Hence, the set of polynomials is not closed under the division operation.
Result:
Possible solution: x ÷ x 2

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?