Question

A rectangle has sides measuring (3x + 5) units and (6x + 11) units.



Part A: What is the expression that represents the area of the rectangle? Show your work to receive full credit.



Part B: What are the degree and classification of the expression obtained in Part A?



Part C: How does Part A demonstrate the closure property for polynomials?

Answer 1

Answer:

Let the length be 3x + 5, let the width be 3x - 4.

The area of a rectangle is length * width.

In this case, it will be(3x + 5)(3x - 4) = 9x^2 + 3x - 20

Answer 2

$\boxed{Part \:A}$

The area is just length times width:

(3x + 5)(6x + 11) = 18x² + 63x + 55

$\boxed{Part \:B}$

The degree of the expression is the highest power which is in 18x²

$\boxed{Part\: C}$

In part A we multiplied 2 polynomials (3x + 5) and (6x + 11) and obtained another polynomial. This demonstrated the closure property of polynomials