MathematicsChapter 4: Factorization and Algebraic Manipulation
What A Factor Is
If an expression equals a product, each piece of that product is a factor.
Learning objectives
- Define and explain what a factor is.
- Apply what a factor is to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
If an expression equals a product, each piece of that product is a factor. 12 = 3 x 4, so 3 and 4 are factors of 12. In algebra, x2 - 9 = (x - 3)(x + 3), so (x - 3) and (x + 3) are factors. Always check by expanding back. A factor may still contain a sum inside it.
Where / symbols
- What A Factor Is
- If an expression equals a product, each piece of that product is a factor. 12 = 3 x 4, so 3 and 4 are factors of 12. In algebra, x^2 - 9 = (x - 3)(x + 3), so (x - 3) and (x + 3) are factors. Always check by expanding back. A factor may still contain a sum inside it.
Overview
Learn the idea, then use it:
Core Understanding
If an expression equals a product, each piece of that product is a factor. 12 = 3 x 4, so 3 and 4 are factors of 12. In algebra, x2 - 9 = (x - 3)(x + 3), so (x - 3) and (x + 3) are factors. Always check by expanding back. A factor may still contain a sum inside it.
Examples product · factor · product of factors · WHAT A FACTOR IS: If an expression equals a product, each piece of that product is a factor. 12 = 3 x 4, so 3 and 4 are factors of 12. In
Exam Application
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Examples Define first · Show the rule or evidence · Check units, labels, and conclusion
WHAT — WHAT A FACTOR IS
If an expression equals a product, each piece of that product is a factor. 12 = 3 x 4, so 3 and 4 are factors of 12. In algebra, x2 - 9 = (x - 3)(x + 3), so (x - 3) and (x + 3) are factors. Always check by expanding back. A factor may still contain a sum inside it.
HOW — Use the idea
Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.
In simple words
Do not merge what a factor is with a neighbouring idea that uses a different definition, rule, or method.
Key points
- product
- factor
- product of factors
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.What A Factor Is
Sticky Notes · Quick Revision
Core Idea
- If an expression equals a product, each piece of that product is a factor.
Key Points
- product
- factor
- product of factors
Simple Check
- Explain what a factor is in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- Do not merge what a factor is with a neighbouring idea that uses a different definition, rule, or method.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- If an expression equals a product, each piece of that product is a factor.
- product
- factor
- product of factors
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