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.Task 1A: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.Task 2Bernard is realizing that his dimensions are not fitting the way that he wants it to because he forgot about the deck. The deck is going to be a rectangular space that borders the pool. Also, for the pool to fit just right, there must be a special product represented when either the area or volume expressions are determined. He wants you to design your own rectangular pool using polynomial expressions, including the deck that borders the pool.A:Include a diagram or sketch of your pool and deck. Your diagram must have all dimensions represented with polynomials and ensure that a special product will be used.B:Determine the polynomial expression to represent the area of land space that the pool will cover.C:Determine the area of the deck that borders the pool based on your dimensions.Task 3Now that you have helped Bernard design the pool, he presents you with a situation. There are x number of communities that will be designing homes with the pools. The number of homes within each community is six more than the number of communities. The number of hours that will be required to build each home is double the number of homes in each community.A:Since x represents the number of communities, determine the two other expressions used to represent the number of homes for each community and the number of hours required to build each home.B:Using the three expressions, interpret the meaning of each grouping of factors as a single unit, and also simplify each expression by finding their product.C:Explain how polynomials demonstrated the closure property throughout this exploration
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