Polynomial Word Problems

Polynomial Word Problems

Read each problem carefully and solve it using your knowledge of polynomial functions and equations. Show all your work.

1. A rectangular box with a square base is to be constructed. The sum of the length of one side of the square base and the height of the box is 10 inches. Express the volume of the box as a polynomial function of the side length of the base. Then, find the dimensions that maximize the volume.

2. A rectangular garden has a length that is 5 feet more than its width. If the area of the garden is 300 square feet, the width of the garden is   feet and the length is   feet.

3. If a polynomial function models the height of a projectile over time, and the function has a positive leading coefficient, the projectile will eventually fall back to the ground.

4. A company's profit P (in thousands of dollars) from selling x units of a product can be modeled by the polynomial function P(x) = -x³ + 15x² - 70x + 120. Which of the following is a possible number of units sold to achieve a profit of $120,000?

5. The population of a certain town can be modeled by the polynomial P(t) = 0.05t³ - 1.2t² + 10t + 5000, where t is the number of years since 2000. In what year (after 2000) does the model predict the population will reach 5000 again?