8th Grade Polynomial Word Problems: Area & Profit Challenges

A farmer has a rectangular field with a length of (3x + 4) meters and a width of (2x + 1) meters. What is the area of the field in terms of x?

• 4x^2 + 7x + 3

• 5x^2 + 10x + 4

• 6x^2 + 9x + 5

• 6x^2 + 11x + 4

A school is organizing a play and needs to arrange seats in rows. If the number of seats in each row is represented by (x^2 + 5x) and there are (x + 2) rows, how many total seats are there?

• x^2 + 5x + 2

• x^3 + 7x^2 + 10x

• x^3 + 10x^2 + 5x

• x^3 + 5x^2 + 2x

A box has a volume represented by the polynomial (x^3 + 2x^2 - 5x) cubic meters. If the height of the box is (x - 1) meters, what is the area of the base in terms of x?

• 2x^2 - 5x + 1

• x^2 - 3x + 2

• x^3 + 2x - 5

• x^2 + 3x - 2

A rectangular garden has a length of (x^2 + 3x) meters and a width of (x + 2) meters. What is the perimeter of the garden?

• 2(x^2 + 2x + 2)

• 2(x^2 + 4x + 2)

• 2(x^2 + 5x)

• 2(x^2 + 3x + 4)

A company produces two types of gadgets. The profit from the first type is represented by (4x^2 + 3x - 2) dollars and from the second type by (2x^2 - x + 5) dollars. What is the total profit in terms of x?

• 4x^2 + 3x + 5

• 2x^2 + 2x - 2

• 5x^2 + 4x + 3

• 6x^2 + 2x + 3

A rectangular swimming pool has a length of (2x + 3) meters and a width of (x + 1) meters. If the pool is filled with water, what is the total area of the surface of the water?

• x^2 + 3x + 1

• 2x^2 + 4x + 2

• 3x^2 + 2x + 5

• 2x^2 + 5x + 3

A recipe requires (x^2 + 4x + 4) cups of flour. If you want to make half the recipe, how much flour do you need in terms of x?

• (1/2)x^2 + 2x + 2

• (1/2)x^2 + 2x + 4

• x^2 + 4x + 4

• (1/2)x^2 + 4x + 4

A car rental company charges a flat fee of (x^2 + 10) dollars plus (3x) dollars per day. What is the total cost for renting the car for x days?

• 5x^2 + 10

• x^2 + 3x + 10

• 3x^2 + 10

• 4x^2 + 10

A rectangular plot of land has a length of (5x - 2) meters and a width of (x + 3) meters. What is the expression for the area of the plot?

• 5x^2 - 13x - 6

• 5x^2 + 15x - 6

• 5x^2 + 13x - 6

• 5x^2 + 10x + 6

A local bakery sells cookies in boxes. If the number of cookies in each box is represented by (x^2 + 2x) and they sell (x + 5) boxes, how many cookies do they sell in total?

• x^3 + 7x^2 + 10x

• 2x^2 + 10x + 5

• x^3 + 5x + 2

• x^2 + 10x + 5