8th Grade Polynomial Puzzles: Factoring & Real-World Context

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 70 square meters, what are the dimensions of the garden?

• Width: 5 meters, Length: 8 meters

• Width: 8 meters, Length: 11 meters

• Width: 7 meters, Length: 10 meters

• Width: 6 meters, Length: 9 meters

A box is designed to hold a volume of 120 cubic centimeters. If the length is twice the width and the height is 3 centimeters less than the width, what are the dimensions of the box?

• Width: 8 cm, Length: 16 cm, Height: 5 cm

• Width: 5 cm, Length: 10 cm, Height: 2 cm

• Width: 4 cm, Length: 8 cm, Height: 1 cm

• Width: 6 cm, Length: 12 cm, Height: 3 cm

The product of two consecutive integers is 72. What are the integers?

• 7 and 8

• 9 and 10

• 6 and 7

• 8 and 9

A school is planning to build a new playground. The area of the playground is represented by the polynomial x^2 + 5x - 24. Factor the polynomial to find the possible dimensions of the playground.

• The possible dimensions of the playground are (x + 8) and (x - 3).

• (x + 6) and (x - 4)

• (x + 10) and (x - 2)

• (x + 5) and (x - 5)

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer pays $70, how many miles did they drive?

• 50 miles

• 150 miles

• 200 miles

• 100 miles

The sum of three consecutive even numbers is 54. What are the numbers?

• 12, 14, 16

• 18, 20, 22

• 16, 18, 20

• 14, 16, 18

A rectangular pool has a length that is 4 meters longer than its width. If the perimeter of the pool is 48 meters, what are the dimensions of the pool?

• Width: 8 meters, Length: 12 meters

• Width: 6 meters, Length: 10 meters

• Width: 10 meters, Length: 14 meters

• Width: 12 meters, Length: 16 meters

A farmer has a rectangular field. The length is represented by the polynomial 2x + 3 and the width by x - 1. What is the area of the field in terms of x?

• 4x + 2

• x^2 + 5x - 3

• 2x^2 + x - 3

• 2x^2 - x + 3

A triangle has a base that is 2 meters longer than its height. If the area of the triangle is 30 square meters, what are the dimensions of the triangle?

• Height: 4 meters, Base: 6 meters

• Height: 6 meters, Base: 8 meters

• Height: 8 meters, Base: 10 meters

• Height: 5 meters, Base: 7 meters

A local bakery sells cupcakes for $2 each and cookies for $1.50 each. If a customer buys a total of 10 items and spends $18, how many cupcakes and cookies did they buy?

• 4 cupcakes and 6 cookies

• 5 cupcakes and 5 cookies

• 7 cupcakes and 3 cookies

• 6 cupcakes and 4 cookies