Question

If the volume of the rectangular prism is represented by 6x2 – 2x + 8 and the base area is 2x – 4, which expression represents the height?

Answer 1

Volume = Base area × height

Height = Volume/Base area.

Volume = 6x² - 2x + 8

Base area = 2x - 4

Height = (6x² - 2x + 8) / (2x - 4)

We use long division of polynomials.

2x - 4 |  6x² - 2x + 8

6x²/2x = 3x

Then : 3x(2x - 4) = 6x² - 12x

(6x² - 2x) - (6x² - 12x) = 10x

10x /2x = 5

5(2x - 4) = 10x - 20

(10x + 8) - (10x - 20) = 28

We have :

3x + 5 + 28/(2x - 4)