Polynomial Area & Volume Problems for Grade 8

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 + 7x + 12

• 2x^2 + 8x + 12

• 2x^2 + 10x + 10

• 2x^2 + 11x + 12

A box has a length of (3x + 2) cm, a width of (x + 5) cm, and a height of (2x) cm. Write a polynomial expression for the volume of the box.

• 6x^3 + 34x^2 + 20x

• 6x^3 + 20x^2 + 15x

• 4x^3 + 20x^2 + 10x

• 5x^3 + 30x^2 + 15x

A school is planning to create a new playground that is (x + 2) meters long and (2x + 1) meters wide. What is the area of the playground?

• 2x^2 + 3x + 1

• x^2 + 4x + 3

• 4x^2 + 2x + 5

• 2x^2 + 5x + 2

A farmer has a field that is (x^2 + 3x) acres. If he wants to plant (x + 2) rows of crops, how many acres will he plant in total?

• (x + 2)(x^2 - 3x)

• (x^2 + 3x)(x - 2)

• (x + 2)(x^2 + 3x)

• (x^2 + 3x) + (x + 2)

A rectangular pool has a length of (4x + 1) feet and a width of (2x - 3) feet. What is the polynomial expression for the area of the pool?

• 8x^2 - 10x - 3

• 4x^2 - 8x + 7

• 10x^2 - 12x + 4

• 6x^2 - 5x + 1

A company produces (x + 1) toys per hour. If they operate for (2x + 3) hours, how many toys do they produce in total?

• x^2 + 4x + 2

• 2x^2 + 5x + 3

• 2x^2 + 3x + 1

• 3x^2 + 2x + 5

A rectangular plot of land has dimensions of (x + 5) meters by (3x - 2) meters. What is the polynomial expression for the area of the plot?

• 3x^2 + 13x - 10

• 4x^2 + 12x - 8

• 2x^2 + 15x - 10

• 3x^2 + 10x - 5

A recipe requires (2x + 1) cups of flour for (x + 3) batches of cookies. How many cups of flour are needed for the total recipe?

• 2x^2 + 5x + 1

• 4x + 9

• 2x^2 + 7x + 3

• x^2 + 3x + 3

A car rental company charges (x + 20) dollars per day. If a customer rents a car for (2x + 5) days, what is the total cost in terms of x?

• 2x^2 + 45x + 100

• 2x^2 + 25x + 50

• x^2 + 30x + 80

• 3x^2 + 40x + 120

A rectangular painting has a length of (x + 4) inches and a width of (3x + 1) inches. What is the area of the painting as a polynomial expression?

• 3x^2 + 12x + 5

• 4x^2 + 15x + 1

• 2x^2 + 10x + 4

• 3x^2 + 13x + 4