Question

The following table shows the length and width of a rectangle: Length Width Rectangle A 3x 5 2x − 3 Which expression is the result of the perimeter of rectangle A and demonstrates the closure property? 10x 4; the answer is a polynomial 2x 4; the answer is a polynomial 10x 4; the answer may or may not be a polynomial 2x 4; the answer may or may not be a polynomial.

Answer 1

Expression giving the result of the perimeter of rectangle A and demonstrating  the closure property is given by: Option A: $10x + 4$ ; the answer is a polynomial

What is the closure property of a polynomial for addition operation?

Closure property keeps the result in the same set.

If two polynomials $f(x)$ and $g(x)$ are there.

Then, $f(x) + g(x) = h(x)$

where $h(x)$ is also a polynomial.

The result of the addition of two polynomials is also a polynomial. This property of polynomial for addition operation is called closure property of a polynomial for addition operation

For the given case, we have:

• Length of the rectangle = $3x + 5$
• Width of the rectangle = $2x -3$

Perimeter of a rectangle with width W and length L = 2(L + W)

And using that formula, the perimeter of the considered rectangle is evaluated as:

$P = 2(3x + 5 + 2x - 3)\\P = 2((3+2)x + 2) = 2(5x + 2)\\\\P = 10x + 4$

Thus, expression giving the result of the perimeter of rectangle A and demonstrating  the closure property is given by: Option A: $10x + 4$ ; the answer is a polynomial

Learn more about addition of polynomials here:

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