Answer:
a. 10x + 4; the answer is a polynomial
Step-by-step explanation:
The perimeter of a rectangle is the sum of the lengths of the 4 sides.
The closure property is that if you add polynomials, the sum is a polynomial.
A rectangle has two congruent lengths and two congruent widths.
Since the length of the rectangle is 3x + 5, there is another length of 3x + 5. The width is 2x - 3, so there is a second width of also 2x - 3.
Let's add the 4 sides together:
3x + 5 + 3x + 5 + 2x - 3 + 2x - 3 =
= 3x + 3x + 2x + 2x + 5 + 5 - 3 - 3
= 10x + 4
The perimeter is 10x + 4. Each side length is a polynomial, and the sum of the all the side length is also a polynomial. This shows there is closure for the addition of polynomials.
Answer: a. 10x + 4; the answer is a polynomial
