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Repeated and Irreducible Factors
Repeated linear factors need every power; irreducible quadratics use a linear numerator.
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Repeated and Irreducible Factors
What is it?
Repeated linear factors need every power; irreducible quadratics use a linear numerator.
In simple words
- Repeated linear factors need every power; irreducible quadratics use a linear numerator.
- Worked pattern: For 1/[x(x-1)^2], include Ax+Bx-1+Cx-12.
- Final check: domain, sign, notation, units, and reasonableness.
Important terms
Repeated and irreducible factors: Repeated linear factors need every power; irreducible quadratics use a linear numerator.
What you should learn
- State the rule for repeated and irreducible factors.
- Solve a repeated and irreducible factors problem step by step.
- Check the result, restrictions, notation, and units.
Recommended for Class 12
Full school-level explanation
Repeated linear factors need every power; irreducible quadratics use a linear numerator.
CONCEPT AND RULE
Repeated linear factors need every power; irreducible quadratics use a linear numerator.
METHOD
For repeated and irreducible factors, identify the given information and required result. Select the matching definition or formula, state its conditions, substitute carefully, simplify one line at a time, and check.
WORKED EXAMPLE
For 1/[x(x-1)2], include Ax+Bx-1+Cx-12.
COMMON MISTAKE
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
How to solve repeated and irreducible factors
How it works
- Identify the mathematical objects, givens, restrictions, and required result.
- Choose and write the relevant definition, theorem, or formula.
- Substitute with brackets and carry out one justified step per line.
- Simplify, state the final answer clearly, and verify it in the original setting.
Remember
- Repeated and irreducible factors
- rule
- worked example
- worked example
How the ideas connect
Worked example: For 1/[x(x-1)^2], include Ax+Bx-1+Cx-12.
Deeper understanding
Go beyond memorising Repeated and Irreducible Factors. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked example: For 1/[x(x-1)^2], include Ax+Bx-1+Cx-12.
Common mistakes
Exam focus
Core Idea
Rule / Formula
Method
Worked Example
Exam focus
Quick revision
- Repeated and irreducible factors
- rule
- worked example
- Repeated and irreducible factors: Repeated linear factors need every power; irreducible quadratics use a linear numerator.
- CONCEPT AND RULE: Repeated linear factors need every power; irreducible quadratics use a linear numerator.
- METHOD: For repeated and irreducible factors, identify the given information and required result. Select the
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
For long answers on Repeated and Irreducible Factors: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- Repeated and irreducible factors
- rule
- worked example
- Repeated and irreducible factors: Repeated linear factors need every power; irreducible quadratics use a linear numerator.
Important formulas
- Repeated and irreducible factors
- rule
- worked example
Common exam traps
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- A matching-looking formula is not valid until its conditions and domain have been checked.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- Mistake
A matching-looking formula is not valid until its conditions and domain have been checked.
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Repeated and irreducible factors
rule
worked example
Repeated and irreducible factors: Repeated linear factors need every power; irreducible quadratics use a linear numerator.
Repeated linear factors need every power; irreducible quadratics use a linear numerator.
- Definition
- Repeated linear factors need every power; irreducible quadratics use a linear numerator.
- Critical warning
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all d
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Exam Practice
Define
Q1. Define Repeated and Irreducible Factors.
Explain
Q2. Explain: CONCEPT AND RULE.
Example
Q3. Give one clear example of Repeated and Irreducible Factors and say why it fits.
Mistake
Q4. State one common mistake students make about Repeated and Irreducible Factors.
Exam note
Q5. Write a short exam note on Repeated and Irreducible Factors: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.