Answer:
Option C is false.
Step-by-step 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
[tex]x^{-6}[/tex]by [tex]x^{2}[/tex]
=> [tex]\frac{x^{-6} }{x^{2} }[/tex]
=> [tex]x^{-6-2}[/tex] =>[tex]x^{-8}[/tex]
This is not a polynomial. So the closure property does not hold true for division of polynomials.
