Factoring and Prime Factorization Concepts

This video tutorial introduces the concept of factoring expressions by identifying and factoring out the greatest common factor (GCF). It emphasizes the importance of finding the GCF as the first step in any factoring problem. The tutorial provides two examples: factoring 5X + 25 and 16X - 24. For each example, the process of identifying the GCF through prime factorization is demonstrated, followed by factoring the expression and verifying the result through distribution.

What is the first step in any factoring problem?

• Find the least common multiple

• Simplify the expression

• Multiply the terms

• Factor out the greatest common factor

What is the greatest common factor of 5X and 25?

• 5

• 25

• 10

• X

After factoring out the GCF from 5X + 25, what is the remaining expression?

• X + 5

• 5X + 5

• X + 25

• 5X + 25

What is the greatest common factor of 16X and 24?

• 24

• 16

• 8

• 4

What is the prime factorization of 16?

• 4 x 4

• 2 x 4 x 2

• 2 x 2 x 4

• 2 x 2 x 2 x 2

What is the prime factorization of 24?

• 3 x 4 x 2

• 2 x 2 x 2 x 3

• 2 x 3 x 4

• 2 x 2 x 6

What is the purpose of writing terms in prime factored form?

• To multiply the terms

• To divide the terms

• To simplify the expression

• To identify common factors

After factoring out the GCF from 16X - 24, what is the remaining expression?

• 2X - 6

• 8X - 6

• 2X - 3

• 8X - 3

How can you verify the correctness of your factoring?

• By dividing the terms

• By distributing the factors

• By multiplying the terms

• By adding the terms

What is the result of distributing the factors in 8(2X - 3)?

• 16X - 3

• 2X - 3

• 8X - 3

• 16X - 24