Factoring and Greatest Common Factors

Mrs. Lopez teaches a Grade 7 lesson on the distributive property and factoring. The lesson begins with a review of the distributive property, followed by an introduction to factoring, where students learn to find common factors and factor expressions. The lesson includes practice problems and advanced techniques using tape diagrams. The concept of rectangular arrays is introduced to help students understand expressions and their factored forms. The lesson emphasizes finding the greatest common factor and converting between standard and expanded forms.

What is the result of applying the distributive property to 2(x + 5)?

• 2x + 5x

• x + 10

• 2x + 10

• 2x + 5

When factoring 5x + 30, what is the greatest common factor?

• 15

• 10

• 30

• 5

How can 8x + 8 be factored using the greatest common factor?

• 4(x + 2)

• 2(4x + 4)

• x + 8

• 8(x + 1)

What is the greatest common factor of 72x + 8?

• 2

• 4

• 8

• 16

In the expression 36x + 4, what is the greatest common factor?

• 6

• 4

• 2

• 8

What is the result of factoring 18x + 12y using the greatest common factor?

• 3(6x + 4y)

• 6(3x + 2y)

• 9(2x + y)

• 2(9x + 6y)

How can the expression 48x + 60y + 24 be factored using the greatest common factor?

• 8(6x + 7.5y + 3)

• 24(2x + 3y + 1)

• 12(4x + 5y + 2)

• 6(8x + 10y + 4)

What is the greatest common factor of 48, 60, and 24?

• 6

• 8

• 12

• 24

Which of the following is a correct factorization of 3x + 3y?

• x + y

• 3x + y

• x + 3y

• 3(x + y)

What is the greatest common factor of 55z + 11?

• 1

• 55

• 11

• 5