[tex]\frac{1}{x}\ .\ x = 1[/tex] does not support the fact that polynomials are closed under multiplication
Solution:
Closure property of polynomials:
Polynomials are always closed under multiplication
The closure property on an operation means that the operation between two elements of a set produce one element of the same set
In this case, the operation is multiplication and the set is the polynomials
Then, the closure property is that the multiplication of two polynomials will always produce a polynomial
From the given options,
[tex]\frac{1}{x}\ .\ x = 1[/tex]
But [tex]\frac{1}{x}[/tex] is not a polynomial
Therefore [tex]\frac{1}{x}\ .\ x = 1[/tex] does not support the fact that polynomials are closed under multiplication
