Grade 8 Polynomial Word Problems

Grade 8 Polynomial Word Problems

Read each word problem carefully and solve for the unknown. Show all your work.

1. The length of a rectangular garden is represented by the polynomial (3x + 5) feet, and its width is represented by (2x - 1) feet. a) Write a polynomial that represents the perimeter of the garden.

b) Write a polynomial that represents the area of the garden.

2. A company's revenue from selling 'x' units of a product is given by the polynomial R(x) = 50x² + 100x. The cost of producing 'x' units is C(x) = 20x² + 50x + 300. The profit P(x) is calculated as Revenue - Cost. Therefore, P(x) =  .

3. The volume of a rectangular prism is given by the expression (x³ + 7x² + 14x + 8). If the length is (x + 1) and the width is (x + 2), what is the height of the prism?

4. The number of cars sold at a dealership in a month can be modeled by the polynomial C(t) = 0.5t² + 10t + 50, where 't' is the number of months since the start of the year. The number of trucks sold in the same month is T(t) = 0.2t² + 5t + 20. Write a polynomial that represents the total number of vehicles sold in a month.

5. If the side of a square is represented by (4x - 2), then its area is 16x² - 16x + 4.