Factoring Polynomials: Real-Life Applications for 9th Grade

A rectangular garden has a length of (x + 5) meters and a width of (x - 2) meters. What is the area of the garden expressed as a polynomial?

• x^2 + 7x - 10

• x^2 + 3x + 10

• x^2 - 3x - 10

• x^2 + 3x - 10

A box is constructed with a volume of (2x^3 + 6x^2 - 8x) cubic meters. If the height of the box is (2x), what is the area of the base expressed as a polynomial?

• x^2 + 3x - 4

• x^2 - 3x + 4

• 2x^2 + 6x - 8

• x^2 + 4x + 1

A farmer has a field represented by the polynomial (3x^2 + 12x). If he wants to plant corn in rows of (3x), how many rows can he plant?

• x + 2

• 2x + 6

• 3x + 4

• x + 4

The area of a triangular plot is given by the polynomial (x^2 + 5x + 6). If the base of the triangle is (x + 2), what is the height expressed as a polynomial?

• 2x + 6

• 3x + 5

• x^2 + 3

• x + 4

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

• 2x^2 + 8x + 2

• 4x^2 + 8x + 2

• 2x^2 + 6x + 4

• x^2 + 4x + 2

A company produces a polynomial profit represented by (4x^2 - 16x). If they want to factor this expression to find the break-even points, what are the factors?

• (4x - 8)(x + 2)

• 4x(x - 4)

• 2x(2 - 8x)

• (2x)(2x - 8)

A school is organizing a play and needs to arrange seats in rows. If the total number of seats is represented by (x^2 + 7x + 10) and each row has (x + 2) seats, how many rows can be formed?

• x + 6

• x + 4

• x + 5

• x + 3

A rectangular piece of land has an area represented by (x^2 - 9) square meters. If one side is (x - 3) meters, what is the length of the other side?

• x + 3

• x^2 - 9

• x - 3

• 3x

A rectangular box has a volume of (x^3 - 4x) cubic meters. If the height is (x), what is the polynomial expression for the area of the base?

• 4x - x^2

• x^2 - 4

• x^3 - 4x

• x^2 + 4

A car rental company charges a flat fee represented by the polynomial (5x + 20) for renting a car. If they want to factor this expression to find the cost per day, what are the factors?

• 10(x + 2)

• 5(x + 4)

• 5(x + 5)

• (5x + 10)(2)