Question

The base of a triangle measures (8x + 2) units and the height measures (4x − 5) 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:

Since

we are given that

Base of triangle = B = (8x + 2)

Height of triangle = H = (4x - 5)

We know that

Area of triangle = (1/2)(base)(Height)

                          = (1/2)(B)(H)

Putting values we get

Area of triangle = (1/2)(8x + 2)(4x - 5) = (4x + 1)(4x - 5)

                          = 16x² - 20x + 4x - 5 = 16x² -16x - 5

Thus

Area of triangle = 16x² -16x - 5

Since

16x² -16x - 5

is the second degree expression so the area is expressed in the second degree polynomial.

And

Since

(4x + 1) and (4x - 5) are polynomials

And

(4x + 1)(4x - 5) = 16x² -16x - 5

Which is again a polynomial so

The Closure law of Multiplication of polynomials hold.