To demonstrate the closure property of polynomials under multiplication, we first need to multiply the two given polynomials [tex]\(5x - 6\)[/tex] and [tex]\(6x + 2\)[/tex]. The closure property states that the product of two polynomials is always a polynomial.
Let's perform the multiplication step-by-step:
1. Multiply each term of the first polynomial by each term of the second polynomial:
[tex]\[
(5x - 6)(6x + 2)
\][/tex]
Using the distributive property (also known as the FOIL method for binomials):
\begin{align}
& \quad (5x - 6)(6x + 2) \\
& = 5x \cdot 6x + 5x \cdot 2 - 6 \cdot 6x - 6 \cdot 2 \\
& = 30x^2 + 10x - 36x - 12
\end{align}
2. Combine like terms:
[tex]\[
30x^2 + 10x - 36x - 12
\][/tex]
[tex]\[
= 30x^2 - 26x - 12
\][/tex]
The result of multiplying the two polynomials [tex]\(5x - 6\)[/tex] and [tex]\(6x + 2\)[/tex] is [tex]\(30x^2 - 26x - 12\)[/tex], which is clearly a polynomial.
Therefore, the statement that correctly shows how the two polynomials demonstrate the closure property when multiplied is:
[tex]\[
30x^2 - 26x - 12 \text{ is a polynomial}
\][/tex]
So the correct answer is:
\[ \boxed{30x^2 - 26x - 12 \text{ is a polynomial}} \
