Factoring Expressions including GCF Word Problems

Factor Expressions and Greatest Common Factor Word Problems

Multiple Choice

Use the GCF to factor the expression 6x + 18 + 12y

• 3(2x + 6 + 4y)

• 8(x + 2 + 3y)

• 6(x + 3 + y)

• 6(x + 3 + 2y)

Multiple Choice

What is the greatest common factor for –9x + 15 + 18y

• 3

• 9

• 15

• 18

Multiple Choice

Factor the expression 25p + 10r

• 2(12p + 5r)

• 5(5p + 2r)

• 5(20p + 8r)

• 5(5p + 10r)

Multiple Select

A hotel manager is adding a tile border around the​ hotel's rectangular pool. Let n represent the width of the​ pool, in feet. The length is 3 more than

3 times the​ width, as shown. Select two expressions that represent the perimeter of the pool.

• 8n + 6

• 8n + 3

• 4(n + 3n + 3)

• 2(4n + 3)

Multiple Choice

Factor the expression 15x - 10xy

• 5(x -2xy)

• 5x(3 - 2xy)

• 5x(3 -2y)

Multiple Choice

For a dinner party, Abraham is creating individual servings of starters. He has 12 carrot sticks, 36 pretzel sticks and 18 celery sticks. If he wants each serving to be identical, with no food left over, what is the greatest number of servings Abraham can create?

• 3

• 6

• 9

• 12

Multiple Select

Which of the following expressions is equivalent to 18+30r​?

Select all that apply

• 2(9 + 15r)

• 6(3 + 5r)

• 6(2 + 15r)

• 3(6 + 15r)

• 9(2 + 6r)

Multiple Choice

Colton has 10 blue marbles, b, 20 green marbles, g and 15 white ones, w. If he wants to place them in identical groups without any marbles left over, choose the expression that could represent the groups that Colton has created.

• 5(2b + 20g + 15w)

• 5(2b + 4g + 3w)

• 10(b + 2g + 5w)

Multiple Choice

Colton has 10 blue marbles, 20 green marbles and 15 white ones. If he wants to place them in identical groups without any marbles left over, what is the greatest number of groups Colton can make?

• 5

• 10

• 15

• 20

Multiple Select

Find the possible dimensions of the sports field given if the width is at least 60 yards. Select all that apply.

• Width 35 yards,

  length 10 - 6d

• Width 60 yards,

  length 6 - 4d

• Width 65 yards,

  length 5 - 3d

• Width 70 yards,

  length 5 - 3d