To demonstrate that polynomials form a closed system under multiplication, we need to show that when we multiply any two polynomials, the result is also a polynomial.
Among the given options:
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- This contains , which is not a polynomial (it's a root). -
- Both and are polynomials. Their product will also be a polynomial. -
- Here, while the terms involved are derived from polynomial expressions, the product simplifies to , which is a polynomial. -
- This is a polynomial by itself, but it doesn't demonstrate closure with another polynomial since it is a standalone expression.
The response that demonstrates closure under multiplication is:
This indicates that the product of the two polynomials is also a polynomial, thereby establishing that polynomials form a closed system under multiplication.