Factoring Polynomials: Area and Volume Applications

A farmer has a rectangular field with an area represented by the polynomial A(x) = x^2 + 5x + 6. If the length of the field is represented by (x + 2), what is the width of the field?

• x + 5

• x + 1

• x + 3

• x + 4

A school is planning to build a new playground. The area of the playground can be represented by the polynomial P(x) = x^2 - 9. If one side of the playground is (x - 3), what is the length of the other side?

• x + 3

• x + 9

• x^2 + 3

• x - 3

A rectangular garden has a length represented by the polynomial L(x) = x^2 + 4x and a width represented by W(x) = x + 2. What is the area of the garden in terms of x?

• x^3 + 6x^2 + 8x

• x^2 + 2x + 8

• x^2 + 6x + 8

• x^3 + 4x^2 + 2

A company produces x^2 - 4x - 12 units of a product. If they can factor this polynomial to find the number of units produced, what are the factors?

• (x - 6)(x + 2)

• (x - 2)(x + 6)

• (x - 4)(x + 3)

• (x - 3)(x + 4)

The height of a triangular banner is represented by the polynomial H(x) = x^2 - 5x + 6. If the base of the banner is (x - 2), what is the height in terms of x?

• x^2 - 6x + 6

• x^2 - 5x + 6

• x^2 - 3x + 5

• x^2 - 5x + 4

A rectangular pool has a length of (x + 3) and a width of (x - 1). Write a polynomial expression for the area of the pool and find its value when x = 4.

• 10

• 15

• 30

• 21

A local artist is creating a mural that can be represented by the polynomial M(x) = x^2 + 3x - 10. If one factor of the mural's design is (x + 5), what is the other factor?

• x - 5

• x + 10

• x - 2

• x + 2

A rectangular plot of land has a polynomial area of A(x) = x^2 + 2x - 8. If one dimension is (x + 4), what is the other dimension?

• x + 2

• x + 8

• x - 2

• x - 4

A rectangular box has a volume represented by V(x) = x^3 - 3x^2 - 4x. If one dimension is (x - 4), what are the other dimensions of the box?

• (x + 4), (x - 3), (x - 1)

• x, (x - 4), (x + 1)

• (x + 4), (x - 1), (x + 2)

• (x - 2), (x + 3), (x + 5)

A local bakery sells cupcakes represented by the polynomial C(x) = x^2 + 6x + 8. If they can factor this polynomial to find the number of cupcakes sold, what are the factors?

• (x + 1)(x + 8)

• (x + 2)(x + 4)

• (x + 3)(x + 5)

• (x + 2)(x + 6)