Factoring Polynomials: Real Applications and Graphing

A rectangular garden has a length of (x + 5) meters and a width of (x - 2) meters. What is the area of the garden in terms of x, and how can you factor this expression?

• x^2 + 7x - 10, factored as (x + 10)(x - 1)

• x^2 + 3x - 10, factored as (x + 5)(x - 2)

• x^2 + 3x + 10, factored as (x + 5)(x + 2)

• x^2 - 3x - 10, factored as (x - 5)(x + 2)

A company produces x^2 - 9 units of a product. If they want to factor this polynomial to find the number of units produced, what are the factors?

• (x - 3)(x - 3)

• (x - 3)(x + 3)

• (x - 4)(x + 4)

• (x - 2)(x + 5)

The height of a triangular banner is represented by the polynomial 2x^2 + 8x. Factor this polynomial to find the height in terms of x, and explain what this means in a real-world context.

• 4(x + 2)

• x(2x + 8)

• 2x(x + 4)

• 2x^2 + 4x

A car's speed can be modeled by the polynomial 3x^2 - 12x. Factor this polynomial to find the speed at which the car is moving, and graph the factored form to show the speed over time.

• (3x^2 - 3x) - 9

• 3x(x - 4)

• 3(x^2 - 4)

• x(3x - 12)

A rectangular pool has a length represented by the polynomial (x^2 + 4x) and a width of (x - 1). Factor the expression for the area of the pool and explain how this relates to the dimensions.

• (x + 4)(x + 1)

• (x^2 - 4)(x - 1)

• x(x + 4)(x + 1)

• x(x + 4)(x - 1)

A farmer has a field represented by the polynomial x^2 + 6x + 8. Factor this polynomial to determine the dimensions of the field, and explain how this could help in planning the layout of crops.

• (x + 1) and (x + 8)

• The dimensions of the field are (x + 2) and (x + 4).

• (x + 3) and (x + 5)

• (x + 2) and (x + 6)

The volume of a box is given by the polynomial x^3 - 3x^2 - 4x. Factor this polynomial to find the dimensions of the box, and graph the factored form to visualize the volume over different dimensions.

• x(x + 4)(x - 1)

• x(x - 2)(x + 2)

• (x - 1)(x + 4)(x + 1)

• x(x - 4)(x + 1)

A school is organizing a play and has a budget represented by the polynomial 5x^2 - 20x. Factor this polynomial to find the budget constraints, and discuss how this could affect the production of the play.

• (5x - 10)(x + 2)

• x(5x - 20)

• 5(x^2 - 4x)

• 5x(x - 4)