Exploring Real-Life Applications of Polynomial Multiplication

A rectangular garden has a length of (2x + 3) meters and a width of (x + 4) meters. What is the area of the garden as a polynomial?

• 2x^2 + 7x + 12

• 2x^2 + 11x + 12

• 2x^2 + 9x + 12

• 2x^2 + 11x + 10

A box has a length of (x + 5) meters, a width of (2x - 1) meters, and a height of (3x + 2) meters. Write a polynomial expression for the volume of the box.

• 5x^3 + 20x^2 + 15x - 5

• 7x^3 + 30x^2 - 3x + 12

• 6x^3 + 31x^2 + 3x - 10

• 4x^3 + 25x^2 + 2x + 1

The perimeter of a rectangular park is represented by the polynomial (2x + 6) + (2x + 8). What is the simplified polynomial expression for the perimeter?

• 4x + 6

• 6x + 8

• 4x + 14

• 2x + 14

A farmer wants to plant a field that is (x^2 + 2x) square meters. If he plants (x + 1) square meters of corn, how much area is left for other crops as a polynomial?

• x^2 + 3x + 1

• x^2 + 2x + 1

• x^2 + x - 1

• x^2 - x + 1

A school is organizing a play and needs to sell tickets. If the price of each ticket is represented by the polynomial (3x + 2) and they sell (x + 4) tickets, what is the total revenue as a polynomial?

• 3x^2 + 12x + 10

• 2x^2 + 8x + 6

• 4x^2 + 10x + 12

• 3x^2 + 14x + 8

A rectangular swimming pool has a length of (3x + 2) meters and a width of (x + 1) meters. What is the polynomial expression for the area of the pool?

• 3x^2 + 5x + 2

• 4x^2 + 3x + 2

• 2x^2 + 4x + 1

• 3x^2 + 2x + 5

A company produces (x^2 - 4) toys each day. If they double their production, what polynomial represents the new production rate?

• 2x^2 - 8

• 4x^2 - 16

• x^2 - 8

• 2x^2 - 4

A rectangular plot of land has dimensions represented by the polynomials (x + 3) and (x - 2). What is the polynomial expression for the area of the plot?

• x^2 + x - 6

• x^2 + 5

• x^2 - x + 6

• x^2 - 5x + 6

A recipe calls for (2x^2 + 3x) cups of flour. If you want to make 3 batches, how much flour do you need in total as a polynomial?

• 9x^2 + 12x

• 2x^2 + 3x

• 6x^2 + 9x

• 4x^2 + 6x

A car rental company charges a base fee of (x + 20) dollars plus (2x) dollars per day. Write a polynomial that represents the total cost for renting a car for x days.

• 2x^2 + 20

• x^2 + 2x + 20

• 2x + 20

• 2x^2 + x + 20