What Is Factorization?
Before we dive into specific techniques, let's make sure we understand what factorization actually means.
The process of writing an algebraic expression as a product of two or more factors. It is the reverse of expanding (multiplying out) brackets.
Think of factorization as the opposite of expansion:
- Expanding:
- Factorizing:
When we factorize, we are asking: "What was multiplied together to give me this expression?"
Factorization is like un-baking a cake — you're figuring out the original ingredients (factors) that were combined (multiplied) to create the final product (the expression).
In this subtopic, we'll learn two powerful factorization techniques:
- Factorization by grouping
- Middle term splitting (for quadratic trinomials)
Quick Review: Taking Out a Common Factor
Before learning grouping and middle term splitting, you need to be confident with the most basic factorization skill — taking out a common factor.
A number, variable, or expression that divides every term of the expression exactly.
To take out a common factor:
- Identify the highest common factor (HCF) of all terms.
- Write the HCF outside brackets.
- Divide each term by the HCF and write the results inside the brackets.
Factorize
- The HCF of and is .
- Divide each term: and .
- Answer:
✅ Check by expanding: ✓
Always check your factorization by expanding the brackets again — you should get back to the original expression.
Quick self-check: Try these before moving on.
- Factorize → Answer:
- Factorize → Answer:
If either of those felt tricky, pause and review common factors before continuing — everything that follows builds on this skill!
13 more sections in this topic
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