Exploring Polynomials: Area, Revenue, and Factoring Fun

A gardener has a rectangular garden with a length of (2x + 3) meters and a width of (x + 4) meters. What is the area of the garden in square meters?

• 2x^2 + 9x + 15

• 2x^2 + 11x + 12

• 2x^2 + 7x + 12

• 3x^2 + 11x + 10

A box has a volume represented by the polynomial V = (x + 2)(x + 3)(x - 1). If the height of the box is (x - 1) meters, what is the area of the base in square meters?

• (x + 2)(x + 3)(x - 1)

• (x + 3)(x - 1)

• (x + 2)(x + 3)

• (x + 2)(x - 1)

A school is organizing a play and needs to sell tickets. The revenue from ticket sales can be represented by the polynomial R = 5x^2 + 20x. If they sell 10 tickets, what is the revenue?

• 600

• 700

• 500

• 800

A rectangular pool has a length of (3x + 5) meters and a width of (2x - 1) meters. What is the polynomial expression for the perimeter of the pool?

• 6x + 4

• 12x + 6

• 10x + 8

• 8x + 10

A farmer is planting a field in the shape of a triangle with a base of (x + 5) meters and a height of (2x - 3) meters. What is the area of the field in square meters?

• 2x^2 + 5x - 10

• 3x^2 - 4x + 8

• x^2 + 2x + 1

• x^2 + 3.5x - 7.5

A car rental company charges a flat fee of $50 plus $20 for each day the car is rented. Write a polynomial expression for the total cost C of renting a car for x days and evaluate it for 3 days.

• 110

• $130

• $150

• $90

A rectangular garden has a length of (x^2 + 2x) meters and a width of (x + 1) meters. Factor the polynomial expression for the area of the garden.

• (x^2 + 3)(x - 1)

• (x + 2)(x + 1)

• x(x + 2)(x + 1)

• x^2 + 3x + 2

A local bakery sells cupcakes for (3x + 2) dollars each. If they sell (x^2 + 4x) cupcakes in a day, what is the polynomial expression for the total sales?

• 4x^3 + 12x^2 + 10x

• 2x^3 + 10x^2 + 6x

• 3x^2 + 8x + 2

• 3x^3 + 14x^2 + 8x

A rectangular plot of land has a length of (x + 6) meters and a width of (x - 2) meters. What is the polynomial expression for the area of the plot, and can you factor it?

• x^2 + 2x - 12; factored form: (x + 6)(x - 2)

• x^2 + 6x - 12; factored form: (x + 3)(x - 4)

• x^2 + 4x - 12; factored form: (x + 6)(x - 2)

• x^2 + 8x - 12; factored form: (x + 4)(x - 3)

A construction company is building a wall that is (x^2 + 5x + 6) meters long. If they want to divide it into sections of (x + 2) meters each, how many sections can they create?

• x + 3

• x + 2

• x + 1

• x + 4