Mastering Grouping: Polynomial Word Problems for Grade 8

A farmer has a rectangular field with an area of 60 square meters. The length of the field is represented by the polynomial expression (x + 5) meters, and the width is (x - 3) meters. Find the value of x using the grouping method to determine the dimensions of the field.

• 8

• 5

• 7

• 10

A school is organizing a play and needs to arrange seats in rows. The total number of seats can be represented by the polynomial expression x^2 + 2x - 8. Use the grouping method to find the number of seats in each row if there are x rows.

• x + 2 and x - 4

• x + 3 and x - 5

• x - 1 and x + 8

• x - 2 and x + 4

A rectangular garden has a length represented by the polynomial (2x + 4) meters and a width represented by (x - 2) meters. If the area of the garden is 48 square meters, use the grouping method to find the value of x.

• 2

• 3√7

• 2√7

• 4√7

A box is to be constructed from a rectangular piece of cardboard with dimensions represented by the polynomial expression x^2 - 9. If the box is to have a volume of 72 cubic meters, apply the grouping method to find the dimensions of the box.

• 2m, 12m, 6m

• 5m, 5m, 3m

• Dimensions of the box are 3m, 9m, and 8m.

• 4m, 6m, 3m

A company produces x^2 + 5x - 14 units of a product. If they want to group the products into boxes of equal size, use the grouping method to find the number of boxes they can create if each box holds x + 2 units.

• x + 4

• x + 5

• x + 1

• x + 3

A rectangular swimming pool has a length of (3x + 6) meters and a width of (x - 2) meters. If the area of the pool is 72 square meters, use the grouping method to find the value of x and the dimensions of the pool.

• x = 1, Length = 9 meters, Width = -1 meter

• x = 3, Length = 15 meters, Width = 1 meter

• x = 4, Length = 12 meters, Width = 2 meters

• x = 2√7, Length = 6 + 6√7 meters, Width = 2√7 - 2 meters

A local bakery sells cookies in packs. The total number of cookies can be represented by the polynomial x^2 - 4x - 12. Use the grouping method to determine how many cookies are in each pack if they are grouped into (x - 6) packs.

• x + 6

• x - 4

• x + 2

• x - 2

A rectangular painting has a length of (x + 7) inches and a width of (2x - 3) inches. If the area of the painting is 50 square inches, apply the grouping method to find the dimensions of the painting.

• Length: 10 inches, Width: 5 inches

• Length: 12 inches, Width: 7 inches

• Length: 15 inches, Width: 3 inches

• Length: 8 inches, Width: 6 inches

A rectangular plot of land has an area represented by the polynomial expression x^2 + 3x - 10. If the length is (x + 5) meters, use the grouping method to find the width of the plot.

• x - 2

• x + 10

• x - 5

• x + 2

A toy manufacturer produces a certain number of toys represented by the polynomial x^2 + 4x - 21. If they want to package the toys in boxes that hold (x - 3) toys each, use the grouping method to find how many boxes they can fill.

• x - 7

• x + 3

• x + 7

• x - 4