
Mastering Grouping: Polynomial Word Problems for Grade 8
Authored by Anthony Clark
English, Mathematics
8th Grade
CCSS covered

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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
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
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
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
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
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
Tags
CCSS.HSA-REI.B.4B
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
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
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
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
Tags
CCSS.HSA.REI.A.2
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
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
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
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
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