Polynomial division can be used to solve a variety of application problems involving expressions for area and volume. We looked at an application at the beginning of this section. Now we will solve that problem in the following example.
The volume of a rectangular solid is given by the polynomial
There are a few ways to approach this problem. We need to divide the expression for the volume of the solid by the expressions for the length and width. Let us create a sketch.
We can now write an equation by substituting the known values into the formula for the volume of a rectangular solid.
To solve for h, first divide both sides by 3x.
Now solve for h using synthetic division.
The quotient is
The area of a rectangle is given by