Factorising grade 10: Common Factor Revision

Summary

In this video, the speaker explains the process of factorization, demonstrating how to factor expressions with varying numbers of terms. They illustrate the importance of identifying common factors among terms, such as coefficients, variables, and powers. Throughout the examples, the speaker emphasizes the technique of taking out the lowest common factor and showcases how to simplify expressions effectively. By working through multiple examples, viewers gain a clear understanding of the factoring process, ensuring they can verify their results by expanding the factored expressions back to their original forms.

Takeaways

• 😀 Factorization involves identifying common factors in numbers and variables, and simplifying expressions by extracting those factors.
• 😀 In the first example, the common factors 3xy were extracted, resulting in the simplified expression 3xy(x + 3).
• 😀 Always take out the greatest common factor (GCF) between the numerical coefficients before considering the variables.
• 😀 When dealing with powers of variables, you can only factor out the lowest exponent present in each term.
• 😀 Factorization helps to break down complex expressions into simpler, more manageable forms, allowing for easier multiplication or solving.
• 😀 To verify factorization, multiply the factored expression back to ensure it matches the original expression.
• 😀 In the second example, the GCF is 3x²y², and the factorized expression is 3x²y²(1 - 2y).
• 😀 In multi-term expressions, identify the smallest power of each variable that appears in all terms to factor them out.
• 😀 In cases where no common factor exists between all terms, you cannot factor them further.
• 😀 Always check if a number can be factored out from all terms, even if only some of the terms share that factor.

Q & A

What is the primary focus of the video?

The video focuses on factorizing algebraic expressions, breaking them down into their components.

What is the first step in factorizing an expression with two terms?

The first step is to identify the greatest common factor (GCF) for the numerical coefficients and variables in both terms.

In the first example, what factors are taken out from the terms 3x²y and 9xy?

From the terms 3x²y and 9xy, the factors taken out are 3, x, and y, resulting in the factored form 3xy(1 + 3x).

How do you determine the common variable to factor out when both terms contain different powers of the same variable?

You take out the variable with the lowest power present in the terms.

In the second example, what is factored out from the terms 3x²y² and 6x²y³?

The common factors are 3, x², and y², leading to the factored expression 3x²y²(1 - 2y).

What should you do if three terms do not have a common numerical factor?

If no common numerical factor exists among three terms, you can factor out the lowest variable that appears in all terms.

What was factored out from the terms 4a²b², 8a³b, and 12ab⁴?

The lowest variable b² was factored out, resulting in the expression b²(4a² + 8a + 12b²).

What is the outcome when factorizing the terms -3x³, -6x², and -9?

The greatest common factor -3 is factored out, yielding the expression -3(x³ + 2x + 3).

How can you verify the accuracy of your factorized expression?

To verify, multiply the factors back together and ensure you obtain the original expression.

Why is it important to consider the lowest power of a variable when factorizing?

It ensures that you only factor out what is common to all terms, allowing for correct simplification and preventing errors.