A right rectangular prism has a volume of {6x}^(3) - {3x}^(2) - 45x What are expressions for the length, width, and height?​

Question

A right rectangular prism has a volume of


`{6x}^(3) - {3x}^(2) - 45x`
What are expressions for the length, width, and height?​

Answer 1

3x, 2x + 5, and x - 3

Explanation:

Since the given figure is a 3-dimensional shape, we know that there must be three zeroes.

Our equation is:

6x³ - 3x² - 45x

First, we can factor out an x:

x (6x² - 3x - 45)

From here, we can see that by factoring out a 3:

3x (2x² - x - 15)

Now, after completing the square and factoring:

3x (2x + 5) (x - 3)

These are our three expressions.