Real-Life Polynomial Applications: Evaluation & Graphing

A gardener has a rectangular garden where the length is represented by the polynomial expression (2x + 3) meters and the width is (x + 1) meters. What is the area of the garden in terms of x?

• 3x^2 + 2x + 1

• 2x^2 + 5x + 3

• x^2 + 6x + 3

• 2x^2 + 4x + 2

A toy company produces a toy that costs (3x^2 + 5x + 2) dollars to manufacture. If they produce 4 toys, what is the total manufacturing cost in terms of x?

• 8x^2 + 12x + 4

• 16x^2 + 25x + 10

• 10x^2 + 15x + 6

• 12x^2 + 20x + 8

A car rental company charges a base fee of (50 - x) dollars plus (20x) dollars for each day rented. How much will it cost to rent a car for x days?

• 50 + 15x

• 50 + 19x

• 50 + 20x

• 30 + 20x

The height of a water tank is modeled by the polynomial (x^2 + 2x + 1) meters. If the tank is filled to a height of 5 meters, what is the value of x?

• 0

• 2

• -2

• -1 + √5 or -1 - √5

A school is planning a field trip and the total cost is represented by the polynomial (100 + 15x) dollars, where x is the number of students. If there are 20 students, what is the total cost?

• 400 dollars

• 300 dollars

• 500 dollars

• 250 dollars

A rectangular swimming pool has a length of (x + 4) meters and a width of (x - 2) meters. Write a polynomial expression for the perimeter of the pool and evaluate it for x = 6.

• 32 meters

• 20 meters

• 24 meters

• 28 meters

A farmer has a field that can be represented by the polynomial (x^2 - 4x + 4) acres. If he wants to plant crops in this field, how many acres will he plant if he uses the expression to find the area?

• (x + 2)(x - 2) acres

• x^2 acres

• (x - 2)^2 acres

• (x - 4)(x + 4) acres

A local bakery sells cupcakes for (2x^2 + 3x) dollars. If they sell 10 cupcakes, how much money do they make in terms of x?

• 10x^2 + 20x

• 25x^2 + 35x

• 20x^2 + 30x

• 15x^2 + 25x

A rectangular plot of land has a length of (3x + 2) meters and a width of (x + 5) meters. What is the polynomial expression for the area of the plot?

• 3x^2 + 17x + 10

• 2x^2 + 15x + 10

• 3x^2 + 20x + 5

• 4x^2 + 10x + 5

A company’s profit can be modeled by the polynomial (x^3 - 3x^2 + 2x - 1) dollars. If they want to evaluate their profit when x = 2, what is the profit?

• -1

• 0

• 5

• -3