Question 3 (Essay Worth 10 points) (06.01, 06.04 MC)
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 (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)

a)

And replacing we got:

And simplifying we got:

b) For this case since the coeficient for the higher degree is 2 then the polynomial is of second degree.

c) We need to remember that the closed property for polynomials tell to us that if we apply any operation between two polynomials we need to obtain and other polynomial. For this special case the property is the sum and after multiply we have another polynomial with a higher degree and then the closed property is satisfied.

Step-by-step explanation:

We know a  rectangle has sides measuring (4x + 5) units and (3x + 10) units

Part a

For this case we can find the area like this:

And replacing we got:

And simplifying we got:

Part b

For this case since the coeficient for the higher degree is 2 then the polynomial is of second degree.

Part c

We need to remember that the closed property for polynomials tell to us that if we apply any operation between two polynomials we need to obtain and other polynomial. For this special case the property is the sum and after multiply we have another polynomial with a higher degree and then the closed property is satisfied.

let m = monomial

let t = trinomial

so, m times t = t.

monomial times a trinomial = another trinomial.