Evaluating and Graphing Polynomials in Real-Life Scenarios

A farmer has a rectangular field where the length is represented by the polynomial expression 2x + 3 and the width is represented by x - 1. What is the area of the field in terms of x?

• x^2 + 2x - 1

• 2x^2 + 5x + 3

• 2x^2 + x - 3

• 4x - 3

A toy company produces a special model of a car that can be represented by the polynomial function f(x) = x^3 - 4x^2 + 6. Evaluate f(2) to find the production cost when 2 models are made.

• 4

• -6

• -2

• 0

The height of a water tank can be modeled by the polynomial h(t) = -t^2 + 5t + 6, where t is the time in hours. What is the maximum height of the tank, and at what time does it occur?

• Maximum height: 8.5 units, Time: 4 hours

• Maximum height: 15 units, Time: 3 hours

• Maximum height: 12.25 units, Time: 2.5 hours

• Maximum height: 10 units, Time: 1 hour

A rectangular garden has a length represented by the polynomial 3x + 2 and a width of x + 4. Write the polynomial expression for the perimeter of the garden and evaluate it for x = 2.

• 24

• 32

• 28

• 30

A local theater's ticket sales can be modeled by the polynomial function p(x) = -2x^2 + 12x + 20, where x is the number of weeks since the opening. Graph this polynomial to find the maximum ticket sales and the week it occurs.

• Maximum ticket sales: 40, occurs at week: 5

• Maximum ticket sales: 25, occurs at week: 4

• Maximum ticket sales: 30, occurs at week: 2

• Maximum ticket sales: 38, occurs at week: 3

A school is planning a dance and the area of the dance floor is represented by the polynomial A(x) = x^2 - 5x + 6. Factor this polynomial to find the dimensions of the dance floor.

• 3 units and 5 units

• 1 unit and 6 units

• 4 units and 2 units

• The dimensions of the dance floor are 2 units and 3 units.

A car's fuel efficiency can be modeled by the polynomial function e(x) = 3x^2 - 12x + 15, where x is the speed in miles per hour. Evaluate e(4) to find the fuel efficiency at that speed.

• 10

• 20

• 5

• 15

The volume of a box can be represented by the polynomial V(x) = x^3 - 2x^2 + 4x. If the box's dimensions are all equal, find the volume when x = 3.

• 18

• 27

• 21

• 15

A company's profit can be modeled by the polynomial function P(x) = -x^2 + 10x - 16. Determine the x-intercepts of this polynomial to find the break-even points.

• x = 1, x = 9

• x = 4, x = 6

• x = 0, x = 10

• x = 2, x = 8

A rectangular swimming pool has a length of (x + 5) meters and a width of (x - 2) meters. Write the polynomial expression for the volume of the pool if the depth is 2 meters and evaluate it for x = 3.

• 16

• 20

• 12

• 10