Grade 12 Polynomial Word Problems Worksheet

Grade 12 Polynomial Word Problems

Read each word problem carefully and solve for the unknown using polynomial equations. Show all your work and provide your answers in the space provided.

1. A rectangular box with a square base is to be constructed from 600 square centimeters of material. Find the dimensions of the box that will maximize its volume. (Let x be the side length of the square base and h be the height.)

2. A farmer has 120 meters of fencing to enclose a rectangular area and divide it into three equal pens with fences parallel to one side of the rectangle. If the area of the pens is to be maximized, the dimensions of the entire rectangular area would be a length of   meters and a width of   meters.

3. The height h (in meters) of a projectile t seconds after it is launched is given by the equation h(t) = -5t² + 40t + 10. At what time does the projectile reach its maximum height?

4. If the population P of a city t years from now is modeled by P(t) = 0.5t³ - 10t² + 50t + 10000, then the population is always increasing after t=0.

5. The cost C (in dollars) of producing x units of a certain product is given by the polynomial C(x) = 0.001x³ - 0.3x² + 50x + 1000. Find the number of units that should be produced to minimize the average cost per unit.