Exploring Polynomials: Area, Volume, and Graphs for Grade 8

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?

• 2x^2 + x - 3

• x^2 + 5x - 1

• 2x^2 + 4x + 3

• 4x^2 + 2x - 3

A toy company produces x^2 + 5x + 6 toy cars each day. If they want to increase production by 4 cars, what polynomial equation represents the new production level?

• x^2 + 5x + 12

• x^2 + 5x + 10

• x^2 + 5x + 8

• x^2 + 5x + 4

A rectangular garden has a length of (x + 4) meters and a width of (x - 2) meters. Write a polynomial expression for the perimeter of the garden and find its value when x = 3.

• 20 meters

• 16 meters

• 12 meters

• 8 meters

The height of a ball thrown into the air can be modeled by the polynomial h(t) = -4.9t^2 + 20t + 5, where t is the time in seconds. What is the maximum height reached by the ball?

• 30.1 meters

• 15.2 meters

• 22.0 meters

• 25.4 meters

A school is planning a dance and expects to sell tickets according to the polynomial equation T(x) = -2x^2 + 30x + 50, where x is the number of days before the dance. How many days before the dance should they sell tickets to maximize ticket sales?

• 5

• 10

• 8

• 12

A rectangular pool has a length of (3x + 2) meters and a width of (x + 1) meters. Write a polynomial expression for the volume of water the pool can hold if the depth is 2 meters. What is the volume when x = 2?

• 40

• 25

• 30

• 50

A company’s profit can be modeled by the polynomial P(x) = 3x^3 - 5x^2 + 2x - 1, where x is the number of units sold. What is the profit when 4 units are sold?

• 150

• 100

• 119

• 80

The cost of producing x items is given by the polynomial C(x) = 2x^2 + 3x + 5. If the company wants to reduce costs by $10, what polynomial equation represents the new cost?

• C'(x) = 2x^2 + 3x - 5

• C'(x) = 2x^2 + 3x + 10

• C'(x) = 2x^2 + 3x + 15

• C'(x) = 2x^2 - 3x + 5

A rectangular box has a length of (x + 5) cm, a width of (2x - 3) cm, and a height of (x - 1) cm. Write a polynomial expression for the volume of the box and find its value when x = 3.

• 30

• 18

• 12

• 24

A local bakery sells cupcakes for a price modeled by the polynomial function P(x) = x^2 - 4x + 8, where x is the number of cupcakes sold. Graph this polynomial function and identify the price when 5 cupcakes are sold.

• $20

• $10

• $15

• $13