Question

The base of a triangle measures (3x − 6) units and the height measures (2x + 4) units. Part A: What is the expression that represents the area of the triangle? Show your work to receive full credit. (4 points) Hint: Area = 0.5bh 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)

Answer 1

Answer With Step-by-step explanation:

Part A:

.5[ (3x – 6) (2x + 4) ]

.5(6x^2 - 24)

3x^2 - 12

Part B:

Second Degree Binomial

Part C:

For Part A, a polynomial was multiplied by another polynomial. The resulting product was a polynomial. This is a demonstration of the closure property for multiplying polynomials.

Answer 2

To answer this item, we use the equation given for the calculation of the area of the triangle.

                                A = 0.5bh

Substituting the known expressions,

                      A = (0.5)(3x – 6)(2x + 4)

 

Part A: Use distribution method to simplify the expression for the calculation of area.

 

                         A = 0.5(6x^2 + 12x – 12x – 24)

                           A = 0.5(6x^2 – 24)

                          A = 3x^2 – 12

 Part B: The equation for area of has a degree of two because the highest exponent is 2.

Part C: The closure property of polynomials is always closed for multiplication.