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Equations Reducible by Factoring
Move all terms to one side, factor, and solve every factor without dividing away solutions.
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Equations Reducible by Factoring
What is it?
Move all terms to one side, factor, and solve every factor without dividing away solutions.
In simple words
- Move all terms to one side, factor, and solve every factor without dividing away solutions.
- Worked pattern: 2sin x cos x-sin x=0 gives sin x=0 or cos x=12.
- Final check: domain, sign, notation, units, and reasonableness.
Important terms
Equations reducible by factoring: Move all terms to one side, factor, and solve every factor without dividing away solutions.
What you should learn
- State the rule for equations reducible by factoring.
- Solve a equations reducible by factoring problem step by step.
- Check the result, restrictions, notation, and units.
Recommended for Class 12
Full school-level explanation
Move all terms to one side, factor, and solve every factor without dividing away solutions.
CONCEPT AND RULE
Move all terms to one side, factor, and solve every factor without dividing away solutions.
METHOD
For equations reducible by factoring, 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
2sin x cos x-sin x=0 gives sin x=0 or cos x=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 equations reducible by factoring
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
- Equations reducible by factoring
- rule
- worked example
- worked example
How the ideas connect
Worked example: 2sin x cos x-sin x=0 gives sin x=0 or cos x=12.
Deeper understanding
Go beyond memorising Equations Reducible by Factoring. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked example: 2sin x cos x-sin x=0 gives sin x=0 or cos x=12.
Common mistakes
Exam focus
Core Idea
Rule / Formula
Method
Worked Example
Exam focus
Quick revision
- Equations reducible by factoring
- rule
- worked example
- Equations reducible by factoring: Move all terms to one side, factor, and solve every factor without dividing away solutions.
- CONCEPT AND RULE: Move all terms to one side, factor, and solve every factor without dividing away solutions.
- METHOD: For equations reducible by factoring, 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 Equations Reducible by Factoring: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- Equations reducible by factoring
- rule
- worked example
- Equations reducible by factoring: Move all terms to one side, factor, and solve every factor without dividing away solutions.
Important formulas
- Equations reducible by factoring
- 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.
Equations reducible by factoring
rule
worked example
Equations reducible by factoring: Move all terms to one side, factor, and solve every factor without dividing away solutions.
Move all terms to one side, factor, and solve every factor without dividing away solutions.
- Definition
- Move all terms to one side, factor, and solve every factor without dividing away solutions.
- 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 Equations Reducible by Factoring.
Explain
Q2. Explain: CONCEPT AND RULE.
Example
Q3. Give one clear example of Equations Reducible by Factoring and say why it fits.
Mistake
Q4. State one common mistake students make about Equations Reducible by Factoring.
Exam note
Q5. Write a short exam note on Equations Reducible by Factoring: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.