Which of the following responses demonstrates that polynomials form a closed system under multiplication?

To demonstrate that polynomials form a closed system under multiplication, we need to show that the product of any two polynomials is also a polynomial.

Let's analyze the options provided:

1. **\( x^2 + 2x + 1 \)**: This is a polynomial by itself, but it does not demonstrate a multiplication of two polynomials.

2. **\( (x + 1) \)**: This is also a polynomial but does not show a product.

3. **\( (2x + 1)(x - 1) \)**: This is a product of two polynomials. When multiplied, it yields \( 2x^2 - 2x + x - 1 = 2x^2 - x - 1 \), which is also a polynomial.

4. **\( (2)(4) \)**: This involves multiplication of two constants, which are technically polynomials of degree 0. However, it does not demonstrate the multiplication of two non-constant polynomials.

The response that best demonstrates the closure of polynomials under multiplication is:

**(2x + 1)(x - 1)**.