# 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.

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.
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Gabriela Werner
The expressions x and ${x}^{2}$ are polynomials. When the expressions are divided, the result is $\frac{1}{x}$ 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: $x÷{x}^{2}$