Name: ______

Application Problems with Polynomials

1. There are two boxes in a storage unit. The volume of the first box is 4x3 + 4x2 cubic units. The volume of the second box is 6x3 - 18x2 cubic units. Write a polynomial for the total volume of the two boxes.

2. The recreation field at a middle school is shaped like a rectangle with a length of 15x yards and a width of 10x - 3 yards. Write a polynomial for the perimeter of the field. Then, calculate the perimeter if x = 2.

3. Two cabins on opposite banks of a river are 12x2 - 7x + 5 feet apart. One cabin is 9x + 1 feet from the river. The other cabin is 3x2 + 4 feet from the river. Write the polynomial that represents the width of the river where it passes between the two cabins. Then, calculate the width ifx = 3.

4. The angle value of Greg's sector can be

modeled by x2 + 6x + 2. The angle value

of Dion's sector can be modeled by 7x + 20.

Which polynomial represents both sectors

combined?

A x2 + x + 18

B x2 + 13x + 22

C 6x2 + 7x + 18

D 7x2 + 6x+ 22

6. The length of a rectangle is 8 centimeters less than 3 times the width.

  1. Write a polynomial that represents the area

of the rectangle.______

  1. Find the area of the rectangle when the

width is 10 centimeters.______

7. A bedroom has a length of x+3 feet and a width of x-1 feet. Write a polynomial to

express the area of the bedroom. Then calculate the area if x = 10.

8. The area of a rectangle is , and the width is . Which expression best
describes the rectangle’s length?

A 3x + 2C 2x + 2

B 2x + 4D 3x – 2

9. Find the volume of a cube with an edge length of 5a2. V = ______

10. The perimeter of a rectangle is 38 centimeters. The length of the rectangle can be represented by (x + 3), and its width can be represented by (2x – 5). What are the dimensions of this rectangle in centimeters?