Lecture Notes: Introduction to Factorization

Overview

• Factorization: Process of rewriting a mathematical expression as a product of two factors.
• Important concept in algebra and relates to simplification.

Key Concepts

Factorization Process

1. Identify Factors
   • For an expression like 3x + 15, identify factors of individual terms.
   • Factors of 3x: 3 and x.
   • Factors of 15: 1 and 15 or 3 and 5.
2. Highest Common Factor (HCF)
   • The first step in factorization is taking out the highest common factor.
   • Identify HCF: The greatest factor that is common between terms.
   • In the example of 3x + 15, the HCF is 3.

Factorization Example

• Expression: 3x + 15
• Steps:
  1. Take Out HCF: Identify the HCF, which is 3.
  2. Rewrite Expression: Divide through by the HCF and open a bracket.
     • Divide 3x by 3: Result is x.
     • Divide 15 by 3: Result is 5.
  3. Final Expression: 3(x + 5)

Strategies and Tips

• Always start factorization by looking for the highest common factor.
• Despite complexity, the method of taking out the HCF remains consistent.
• Key Rule: Once factorized, the expression should be represented as a product of factors.

Conclusion

• Factorization simplifies expressions by reducing them to a product of factors.
• Practice with increasing complexity, applying the same method.
• Reminder: Follow the steps diligently to handle challenging questions.

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