A rectangle has sides measuring (4x + 5) units and (3x + 10) units. Part A: What is the expression that represents the area of the rectangle? Show your work to receive full credit. (4 points)

Part B: What are the degree and classification of the expression obtained in Part A? (3 points)

Part C: How does Part A demonstrate the closure property for polynomials? (3 points)

see below

Step-by-step explanation:

A = l*w

A = (4x+5)(3x+10)

FOIL

  = 4x*3x + 4x*10 + 5*3x+ 5*10

   = 12x^2 + 40x +15x+50

Combine like terms

   = 12x^2+55x+50

The degree is the highest power of x which is 2 so it is a quadratic

The classification is the number of terms, which is 3 so it is a trinomial

The degree and classification is a quadradic trinomial

We started with two polynomials and multiplied.  We ended with a polynomial.  Since we produced another polynomial under the operation of multiplication using two polynomials in the set, this demonstrates the closure property for polynomials

a negative exponent is translated as follows:

so, we have