Answer:
The expression for the height of the solid is:
Explanation:
Recall that the volume of a rectangular solid is given by:
Where l is the length, w is the width, and h is the height.
We know that the volume is given by the polynomial:
And that the length and width are given by, respectively:
Substitute:
We can solve for h. First, divide both sides by 3x:
Divide each term:
To solve for h, divide both sides by (x - 2):
Since this is a polynomial divided by a binomial in the form of (x - a), we can use synthetic division, where a = 2. This is shown below. Therefore, the expression for the height of the solid is: