Greatest Common Factor and Factoring

This video tutorial explains how to factor expressions using the greatest common factor (GCF) and the distributive property. It begins with an introduction to factoring and the concept of GCF, followed by examples to illustrate these concepts. The tutorial then demonstrates how to factor the expression 4x + 8 using algebra blocks and the standard algorithm. It concludes by addressing common mistakes made when factoring expressions, emphasizing the importance of using the correct GCF.

What is the greatest common factor (GCF)?

• The difference between the largest and smallest factors

• The sum of all factors of a number

• The largest factor two numbers have in common

• The smallest factor two numbers have in common

Which of the following is a factor of 24?

• 7

• 9

• 8

• 5

What is the GCF of 24 and 32?

• 4

• 6

• 12

• 8

What does the distributive property help with in expressions?

• Expanding and factoring expressions

• Subtracting terms

• Dividing terms

• Adding terms

How do you expand the expression 3(x + 4)?

• 3x + 4x

• 3x + 7

• 3x + 12

• 3x + 4

What is the GCF of 4x and 8?

• 4

• 3

• 2

• 1

How can 4x + 8 be factored using the GCF?

• 4(x + 2)

• 2(x + 4)

• x(4 + 8)

• 8(x + 1)

What is a common mistake when factoring expressions?

• Not using any factor

• Using the smallest factor

• Using the sum of factors

• Not using the greatest common factor

Which expression is completely factored: 4x + 8 or 2(2x + 4)?

• Neither is completely factored

• 4x + 8

• 2(2x + 4)

• Both are completely factored

Why is it important to use the GCF in factoring?

• To remove all parentheses

• To ensure the expression is completely factored

• To make the expression longer

• To add more terms to the expression