Factoring and Greatest Common Factor

The video tutorial explains how to factor expressions by identifying and extracting the greatest common factor (GCF). It demonstrates the process using three examples: two-x plus eight, twelve-x minus fifteen, and sixteen-y minus twenty-four. The tutorial emphasizes the importance of prime factorization in identifying the GCF and verifies the correctness of the factored expressions by distributing back to the original form.

What is the first step in factoring an expression by its greatest common factor?

• Add all terms together

• Identify the greatest common factor

• Multiply all terms by two

• Divide all terms by the smallest number

Which of the following is a method to find the greatest common factor?

• Multiplying all terms

• Adding all terms

• Prime factorization

• Subtracting the smallest term

What is the greatest common factor of the terms 2x and 8?

• 2

• 4

• 8

• x

After factoring out the GCF from 2x + 8, what is the resulting expression?

• x + 4

• 2(x + 4)

• x + 8

• 2x + 4

What is the result of distributing the factor back into the expression 2(x + 4)?

• x + 4

• x + 8

• 2x + 4

• 2x + 8

What is the greatest common factor of the terms 12x and 15?

• 12

• 3

• 15

• 5

What is the factored form of 12x - 15?

• 12x - 5

• 3x - 15

• 4x - 5

• 3(4x - 5)

What is the result of distributing the factor back into the expression 3(4x - 5)?

• 3x - 15

• 4x - 5

• 12x - 15

• 12x - 5

What is the greatest common factor of the terms 16y and 24?

• 4

• 8

• 24

• 16

What is the factored form of 16y - 24?

• 8(2y - 3)

• 2y - 3

• 8y - 24

• 16y - 3