Question

Which of the following statements about closure is false?

Answer 1

Option C is false.

Explanation:

The correct answer is:

C. Polynomials are closed under division. When you divide polynomials, the result will always be a polynomial.

This is false because sometimes when we divide polynomials, one polynomial does not gets completely or evenly divided by the other.

In such cases, we get a remainder which is not a monomial as the variable has a negative power. This means the quotient is not a polynomial.

We can show this by example : suppose we want to divide

`x^(-6)`by
`x^(2)`

=>
`(x^(-6) )/(x^(2) )`

=>
`x^(-6-2)` =>
`x^(-8)`

This is not a polynomial. So the closure property does not hold true for division of polynomials.