Question

A rectangle has sides measuring (2x + 7) units and (5x + 9) units.

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

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

Part A:

(2x+7)(5x+9)

(2x*5x)+(2x*9)+(7*5x)+(7*9)

10x^2+18x+35x+63

10x^2+53x+63

Part B:

The polynomial has two terms, so is a binomial; also, the polynomial only has one variable, x, and the largest exponent of that variable is 2; therefore is a degree 2 polynomial. In summary, we have a binomial of degree 2.

Part C: Part A demonstrates the closure property for polynomials because after multiplying the polynomials we obtained another polynomial.

Explanation: