Applying Understanding of Polynomials
The diagram below represents the Jane’s spring garden plan. Although you might never see a garden with these measures (in terms of a variable), you will use your knowledge of the computation and simplification of polynomials to answer the questions below.
- Write and simplify a polynomial expression that represents the south side of the field.
- Write polynomial expressions that represent: the perimeter of the carrot patch and the perimeter of the lettuce patch.
- Find the area of the same two patches mentioned in question two.
- Assume that \(x=4\), determine the perimeter and area of the carrots patch. Dimensions are in feet.
- Jane would like to plant three additional patches of produce. Using factoring, determine possible dimensions of each of the patches below:
a. The area of the strawberry patch is \(16x^2+4x\).
b. The area of the cucumber patch is \(x^2-4x-21\).
c. The area of the tomato patch is \(x^2-36\).
- Jane is adding a zucchini patch that has dimensions that are half those of the watermelon patch. Find and simplify polynomials that would represent the dimensions of the zucchini patch.