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

To determine which of the provided responses demonstrates that polynomials form a closed system under multiplication, we need to ensure that multiplying any two polynomials results in a polynomial.

1. **(x)(6x • -3)**: This is an expression involving multiplication of polynomials:
- The term \(6x\, \cdot\, -3\) is a polynomial (specifically, \(-18x\)), and multiplying it by another polynomial (the variable \(x\)) gives \(-18x^2\), which is also a polynomial.

2. **3х^2/4 - 1**: This expression contains a polynomial \(3x^2/4\) and a constant \(-1\), but it is not presented in a multiplicative context, so it doesn't demonstrate closure under multiplication.

3. **(х)(1/2х)**: In this case, you're multiplying two polynomials:
- \(x\) is a polynomial, and \(1/2x\) is also a polynomial (specifically, it can be viewed as \( \frac{1}{2}x^1\)).
- Their product is \((1/2)x^2\), which is a polynomial.

4. **1/4x^3 • 5**: This multiplication involves \(1/4x^3\) (a polynomial) multiplied by \(5\) (also considered a polynomial as it can be seen as \(5x^0\)). The product is \((1/4 \cdot 5)x^3 = \frac{5}{4}x^3\), which is a polynomial.

Based on these evaluations, the responses that clearly show closure under multiplication of polynomials are:

- **(x)(6x • -3)**
- **(х)(1/2х)**
- **1/4x^3 • 5**

Each of these involves multiplying polynomials to yield another polynomial. The expression **3х^2/4 - 1** does not represent a multiplication operation. Therefore, **all three multiplicative expressions (1, 3, and 4)** demonstrate that polynomials form a closed system under multiplication.