11th Grade Polynomial Problem Solving & Factoring Challenge

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 70 square meters, find the dimensions of the garden by solving the polynomial equation.

• Width: 5 meters, Length: 8 meters

• Width: 7 meters, Length: 10 meters

• Width: 6 meters, Length: 9 meters

• Width: 8 meters, Length: 11 meters

A car's value decreases according to the polynomial function V(t) = -2000t^2 + 12000t + 30000, where V is the value in dollars and t is the time in years. Determine when the car will be worth $0 by solving the polynomial equation.

• 12 years

• 5 years

• 15 years

• 9 years

The height of a triangular prism is 2 meters less than twice the base length. If the volume of the prism is 48 cubic meters, express the volume as a polynomial equation and find the base length.

• 10

• 6

• 12

• 8

A company produces a certain product, and the profit P (in dollars) can be modeled by the polynomial P(x) = -5x^2 + 150x - 200, where x is the number of units sold. Determine the number of units that must be sold to maximize profit by solving the polynomial equation.

• 15

• 20

• 10

• 25

The length of a rectangular pool is 4 meters more than twice its width. If the perimeter of the pool is 48 meters, find the dimensions of the pool by solving the polynomial equation.

• Width: 5 meters, Length: 14 meters

• Width: 15 meters, Length: 34 meters

• Width: 20/3 meters, Length: 52/3 meters

• Width: 10 meters, Length: 24 meters

A ball is thrown into the air, and its height h (in meters) after t seconds is given by the polynomial h(t) = -4.9t^2 + 20t + 1. Determine when the ball will hit the ground by solving the polynomial equation.

• 3.25 seconds

• 2.75 seconds

• 5.00 seconds

• 4.14 seconds

A farmer has a rectangular field where the length is 5 meters less than three times the width. If the area of the field is 150 square meters, find the dimensions of the field by solving the polynomial equation.

• Width: 10 meters, Length: 25 meters

• Width: 15 meters, Length: 30 meters

• Width: 5 meters, Length: 20 meters

• Width: 12 meters, Length: 18 meters

The revenue R (in dollars) from selling x items is given by the polynomial R(x) = 50x - 0.5x^2. Determine the number of items that need to be sold to achieve a revenue of $1000 by solving the polynomial equation.

• 72 or 28

• 60 or 40

• 10 or 90

• 50 or 100

A rectangular box has a volume of 120 cubic centimeters. If the length is 2 centimeters more than the width and the height is 3 centimeters less than the width, find the dimensions of the box by solving the polynomial equation.

• Width: 6 cm, Length: 8 cm, Height: 3 cm

• Width: 5 cm, Length: 7 cm, Height: 4 cm

• Width: 10 cm, Length: 12 cm, Height: 8 cm

• Width: 4 cm, Length: 6 cm, Height: 5 cm

The height of a water tank is 3 meters more than its radius. If the volume of the tank is 100π cubic meters, express the volume as a polynomial equation and find the radius of the tank.

• 6

• 3

• 5

• 4