Grade 8 Polynomial Word Problems: Multiply & Factor

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

• 2x^2 + 11x + 12

• 2x^2 + 7x + 12

• x^2 + 5x + 12

• 2x^2 + 11x + 10

A box has a volume represented by the polynomial (3x^2 + 6x) cubic meters. If the height of the box is (x + 2) meters, what is the area of the base in terms of x?

• 3x^2

• 3x

• 6x

• x^2 + 2

The perimeter of a rectangular park is represented by the polynomial (4x + 20) meters. If the length is (2x + 5) meters, what is the width of the park in terms of x?

• 5

• 10

• 2x + 10

• 15

A school is selling tickets for a play. The total revenue from ticket sales can be represented by the polynomial (5x^2 + 15x) dollars, where x is the number of tickets sold. If each ticket costs (x + 3) dollars, how many tickets were sold?

• 3

• 5

• 10

• 7

A farmer has a field that can be represented by the polynomial (x^2 + 5x + 6) acres. If he wants to plant corn in a section that is (x + 2) acres, how much area will be left for other crops?

• (x + 3)(x + 1) acres

• (x^2 + 3x + 4) acres

• (x + 2)(x + 2) acres

• (x^2 + 4x + 5) acres

The area of a triangular plot of land is represented by the polynomial (x^2 + 4x) square meters. If the base of the triangle is (x + 2) meters, what is the height of the triangle in terms of x?

• x^2 + 4

• 2x + 4

• x + 2

• 2x + 2

A rectangular swimming pool has a length of (x + 5) meters and a width of (2x - 1) meters. What is the expression for the area of the pool in terms of x?

• 4x^2 - 3x + 1

• x^2 + 7x + 5

• 2x^2 + 10x - 5

• 2x^2 + 9x - 5

A company produces a polynomial profit represented by (2x^2 + 8x - 10) dollars, where x is the number of units sold. If the cost to produce each unit is represented by (x + 1) dollars, how can the profit be factored?

• 2(x + 1)(x + 10)

• 2(x + 5)(x - 1)

• (x + 2)(2x - 5)

• (x - 2)(2x + 5)

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

• 8x + 6

• 4x + 3

• 10x + 8

• 6x + 4

A local bakery sells cookies in boxes. The total number of cookies can be represented by the polynomial (x^2 + 3x + 2). If each box contains (x + 1) cookies, how many boxes can be filled?

• x + 1

• 2x + 2

• x + 3

• x + 2