Question

The volume of a rectangular prism is (x{3} – 3x{2} + 5x – 3), and the area of its base is (x{2} – 2). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?

Answer 1

A)x-3 + 7x-9/x^2-2

Explanation:

Answer 2

x³ - 3x² + 5x - 3 / x² - 2

Explanation:

Given in the question,

volume of a rectangular prism = x³ - 3x² + 5x - 3

base area of a rectangular prism = x² - 2

Formula for the volume of prism

V = BA x H

here BA is base area

H is height

Formula for the height of prism

H = V / BA

plug values in the formula

x³ - 3x² + 5x - 3 / x² - 2

We will do long division

x - 1

----------------------------

x² - 2 | x³ - 3x² + 5x - 3

x³ - 2x²

---------------------------

-x² + 5x - 3

-x² + 2

----------------------

5x - 5

The remainder indicates that x³ - 3x² + 5x - 3 is not divisible by x² - 2, and that means that you cannot find the exact height.