To determine the perimeter of rectangle [tex]\( A \)[/tex], we need to apply the formula for the perimeter of a rectangle, which is [tex]\( P = 2 \times (\text{Length} + \text{Width}) \)[/tex].
Given:
- Length [tex]\( = 4x + 5 \)[/tex]
- Width [tex]\( = 3x - 2 \)[/tex]
Let's calculate the perimeter step-by-step.
1. Find the sum of the length and the width:
[tex]\[
\text{Length} + \text{Width} = (4x + 5) + (3x - 2)
\][/tex]
2. Combine the like terms:
[tex]\[
(4x + 3x) + (5 - 2) = 7x + 3
\][/tex]
3. Multiply the sum by 2 to find the perimeter:
[tex]\[
P = 2 \times (7x + 3)
\][/tex]
4. Distribute the 2 to each term inside the parentheses:
[tex]\[
P = 2 \times 7x + 2 \times 3 = 14x + 6
\][/tex]
So, the expression for the perimeter of rectangle [tex]\( A \)[/tex] is [tex]\( 14x + 6 \)[/tex].
Now, regarding whether this expression demonstrates the closure property:
- The closure property in the context of polynomials states that the sum, difference, and product of polynomials is also a polynomial.
- Since [tex]\( 14x + 6 \)[/tex] is an expression that is linear in form (a polynomial of degree 1), it demonstrates the closure property when considering addition and multiplication of polynomials.
Thus, the expression [tex]\( 14x + 6 \)[/tex] is a polynomial, and the correct answer from the given options is:
[tex]$14x + 6$[/tex]; the answer is a polynomial.
