Which of the following options correctly describes if the following polynomial forms a closed system under multiplication? −3(5x+4y)=−15x−12y Option #1: Yes, because the result of multiplying the polynomials is also a polynomial. Option #2: No, because the exponent of x is not a positive integer. Option #3: No, because multiplying the polynomials resulted in subtraction. (1 point)

To determine if the given polynomial forms a closed system under multiplication, we examine the expression provided:

\(-3(5x + 4y) = -15x - 12y\)

This expression shows a polynomial that results from multiplying a constant \(-3\) by the polynomial \(5x + 4y\).

Now let's analyze the options:

- **Option #1:** "Yes, because the result of multiplying the polynomials is also a polynomial."
- This statement is correct. The result \(-15x - 12y\) is indeed a polynomial, as it is a linear combination of the variables \(x\) and \(y\).

- **Option #2:** "No, because the exponent of x is not a positive integer."
- This statement is incorrect. While one term in a polynomial contains a variable raised to the first power, it is still a polynomial. A polynomial can include terms with non-negative integer exponents, and \(x^1\) is a valid term in a polynomial.

- **Option #3:** "No, because multiplying the polynomials resulted in subtraction."
- This statement is also incorrect. Subtraction is allowed in polynomial expressions, and forming a polynomial through operations that include subtraction does not preclude the result from being a polynomial.

Thus, the correct answer is **Option #1:** Yes, because the result of multiplying the polynomials is also a polynomial.