Question

At times, it is necessary to make plans even when all of the facts are not there. Bernard is currently facing such a dilemma. Bernard is asked to create a swimming pool and deck design for a new series of model homes currently being designed. Each home will have varying pool sizes depending on the lot size; however, there will be some similarities, so polynomial expressions will be used. Your task will be to help Bernard.
To fit the dimensions of the various land spaces, he realizes that the length of the pool has to be three times the size of the width plus 3 and the depth has to be 7 less than twice the length.


A. Create a variable to represent the width of the pool. Determine the expressions to represent length and the depth in terms of the width variable.

B.Determine the polynomial expression to represent the area of land space that the pool will cover.

C.Using the area and the depth expressions, determine the polynomial expression that is used to represent the volume.

D.Classify the volume polynomial by degree and number of terms.

Answer 1

A. Let us assume the width of the pool = x
Then
Length of the pool = 3x + 3
Depth of the pool = 2(3x + 3) - 7
                            = 6x + 6 - 7
                            = 6x - 1
B. Area of the land space = Width * length
                                          = x * (3x + 3)
                                          = 3x^2 + 3x
C. Volume of the pool = (6x - 1) * (3x^2 + 3x)
                                    = 18x^3 + 18x^2 - 3x^2 - 3x
                                    =  18x^3 + 15x^2 - 3x
 D. The highest degree is actually 3 and the number of terms that we get is also 3.