Exploring Polynomial Factors in Real-Life Scenarios

A gardener is planting flowers in a rectangular garden. The area of the garden is represented by the polynomial A(x) = x^2 + 5x + 6. If the length of the garden is (x + 2), what is the width of the garden?

• x + 4

• x + 1

• x + 5

• x + 3

A school is organizing a play and needs to arrange seats in rows. The total number of seats can be represented by the polynomial S(x) = x^2 - 4x - 12. If each row has (x - 6) seats, how many rows are there?

• x + 6

• x + 2

• x - 2

• x - 4

A factory produces x^2 + 3x - 10 units of a product. If the production can be factored as (x + 5)(x - 2), how many units does the factory produce when x = 3?

• 5

• 0

• 8

• 10

A rectangular pool has a length represented by the polynomial L(x) = x^2 + 2x and a width of (x + 1). What is the area of the pool in terms of x?

• x^3 + 2x^2 + 1

• x^2 + 2x + 1

• x^3 + x^2 + 2x

• x^3 + 3x^2 + 2x

A farmer has a field with an area represented by the polynomial F(x) = 2x^2 + 8x. If the length of the field is (2x), what is the width of the field?

• 2x + 4

• x + 4

• x + 2

• 2x + 2

A company sells x^2 - 9 units of a product. If the product can be factored as (x - 3)(x + 3), how many units does the company sell when x = 5?

• 20

• 16

• 25

• 10

A rectangular garden has an area of A(x) = 3x^2 + 12x. If the length is (3x), what is the width of the garden?

• 3x + 4

• x + 4

• 2x + 6

• x + 2

A box has a volume represented by the polynomial V(x) = x^3 - 4x^2 + 4x. If the height of the box is (x), what is the area of the base in terms of x?

• 4x - x^2

• x^2 - 4x + 4

• x^2 - 2x

• x^3 - 4x

A car rental company charges a flat fee represented by the polynomial C(x) = x^2 + 6x + 8. If the fee can be factored as (x + 2)(x + 4), what is the cost when x = 3?

• 30

• 40

• 25

• 35

A construction company is building a wall with an area represented by the polynomial W(x) = x^2 - 5x + 6. If the width of the wall is (x - 2), what is the height of the wall?

• x - 5

• x - 4

• x - 3

• x - 2