Question

Now 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.

Answer 1

To answer the following questions:

a) Number of homes for each community = x + 6
Number of hours required to build each home = 2 (x + 6)
Number of houses altogether = x2 + 6x

b) 2x3 + 24x2 + 72x

c) All the generated products are polynomials. Using multiplication on polynomials will yield a closed set of polynomials because multiplying them with yield another polynomial.

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