Factorization Concepts and Verification

In this video, Daniel Carreón introduces the concept of factorization by common factor. He explains the process through three examples: 4a + 5ab, 5x² + 7x³ - 3x, and 10a + 6a². Each example is broken down step-by-step, demonstrating how to identify and extract the common factor, and verify the factorization by multiplying back. The video concludes with a call to action for viewers to try additional exercises and engage with the content.

What is the primary goal of factorization by common factor?

• To eliminate variables from expressions

• To convert expressions into fractions

• To decompose expressions into a product

• To simplify expressions by addition

In the expression 4a + 5ab, what is the common factor?

• b

• a

• 5

• 4

After factorizing 4a + 5ab, what expression do we get inside the parentheses?

• 4 + 5b

• 4a + 5

• a + b

• 4a + 5ab

How do we verify the correctness of a factorized expression?

• By adding the terms

• By dividing the terms

• By multiplying back the factors

• By subtracting the terms

In the expression 5x² + 7x³ - 3x, what is the common factor?

• 7

• x

• 3

• 5

What is the result of factorizing 5x² + 7x³ - 3x?

• x(5 + 7x - 3)

• 5x + 7x² - 3

• 5x² + 7x³ - 3x

• x(5x + 7x² - 3)

In the expression 10a + 6a², what is the numerical common factor?

• 10

• 6

• a

• 2

What is the factorized form of 10a + 6a²?

• 10a + 6a²

• a(10 + 6a)

• 2a(5 + 3a)

• 2(5a + 3a²)

Why is it important to verify the factorization?

• To validate the original expression

• To ensure the expression is simplified

• To confirm the expression is a product

• To check if the expression is correct

What should be done if the factorization is incorrect?

• Change the expression

• Ignore the error

• Add more terms

• Recalculate the factors