MathematicsChapter 5: Polynomials
Division Algorithm
Divide by a linear x-c: remainder is a constant.
Learning objectives
- State the rule or meaning of division algorithm in easy words.
- Apply division algorithm in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Definition
Divide by a linear x-c: remainder is a constant. Long division or synthetic (later). Stop when the leftover degree is less than the divisor's degree.
Where / symbols
- DIVISION ALGORITHM
- Divide by a linear x-c: remainder is a constant. Long division or synthetic (later). Stop when the leftover degree is less than the divisor's degree.
- DIVISION ALGORITHM
- Divide by a linear x-c: remainder is a constant.
Relationship
- degree = highest power
Overview
Understand the idea, then apply it:
Main Idea
Divide by a linear x-c: remainder is a constant. Long division or synthetic (later). Stop when the leftover degree is less than the divisor's degree.
Examples Like integers · Linear divisor: r = number · p = q d + r
Exam Use
Write the rule first: Divide by a linear x-c: remainder is a constant. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Examples State the central idea · Use one accurate detail · Check the final response
WHAT — DIVISION ALGORITHM
Divide by a linear x-c: remainder is a constant. Long division or synthetic (later). Stop when the leftover degree is less than the divisor's degree.
WHY — Why it matters
This rule is a separate learning unit inside polynomials and division. It can be defined, applied, and checked in its own FBISE question.
HOW — How to answer
Write the rule first: Divide by a linear x-c: remainder is a constant. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
How to answer a division algorithm question
- Read the exact command word and identify what the question asks.
- State the matching idea, rule, or meaning before adding detail.
- Use the unit evidence or mathematical working that directly supports the answer.
- Check accuracy, relevance, and answer length before finishing.
In simple words
1x and sqrt(x) are not polynomials. Powers must be 0,1,2,...
Key points
- r smaller degree
- degree = highest power
- divide: quotient + remainder, deg r smaller
- focused answer
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Division Algorithm
Sticky Notes · Quick Revision
Core Idea
- Divide by a linear x-c: remainder is a constant.
What to Know
- Divide by a linear x-c: remainder is a constant. Long division or synthetic (later). Stop when the leftover degree is less than the divisor's degree.
Example or Evidence
- Like integers
- Linear divisor: r = number
- p = q d + r
How to Answer
- Write the rule first: Divide by a linear x-c: remainder is a constant. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Common Error
- 1x and sqrt(x) are not polynomials. Powers must be 0,1,2,...
FBISE Exam Check
- State the rule, show the working, and check the answer.
60-second revision
- Divide by a linear x-c: remainder is a constant.
- Like integers
- Linear divisor: r = number
- State the rule, show the working, and check the answer.
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