How To Solve LCM in Polynomials

Duration: 13 min

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Module outline

  1. About the Course: About the Course
  2. Section 1 | भाषा (हिंदी) / Language (Hindi): भाषा, लिपि और वर्ण, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, पद-भेद और रूप-विकार, लिंग, वचन, पुरुष और कारक, काल, वाच्य, वाक्य और वाक्य-भेद, संधि, समास, विलोम शब्द, पर्यायवाची शब्द, सामान्य अशुद्धियाँ, अनेक शब्दों के लिए एक शब्द, शब्द-भंडार, अपठित बोध, बहुविषयक सामग्री (विभिन्न अवधारणाओं से संबंधित सामग्री), वर्णमाला
  3. Section 1 | اردو زبان / Language (Urdu) — 22 Questions (Fixed): رسم الخط، حروفِ تہجی اور املا, اسم، ضمیر اور صفت, الفاظ، محاورے اور ضرب الامثال, تفہیمِ عبارت، انشا اور ترجمہ, تفہیم
  4. Section 1 | বাংলা ভাষা / Language (Bengali) — 22 Questions (Fixed): শব্দার্থ, বাগধারা ও ভাষাশুদ্ধি, বাক্য ও বাচ্য, শব্দগঠন ও শব্দভান্ডার, অনুবাদ, বোধপরীক্ষণ ও রচনা
  5. Section 1 | Language (English): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Verbs and Tenses, Pronoun, Verb, Adverb, Prepositions and Conjunctions, Parts of Speech, Determiner, Conjunction, Modals, Transformation of Sentences, Direct and Indirect Speech, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Sentence Structure and Common Errors, Reading Comprehension, Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Facts, Inference and Judgements
  6. Section 2 | Primary Maths & Reasoning / प्राथमिक गणित एवं तर्कशक्ति: Ratio and Proportion / अनुपात और समानुपात, Divisibility Rules / विभाज्यता के नियम, Mixture and Alligation / मिश्रण और एलिगेशन, Permutation and Combination / क्रमचय और संचय, Number System / संख्या पद्धति, HCF and LCM / महत्तम समापवर्तक और लघुत्तम समापवर्त्य, Sequences, Series and Combinatorics / अनुक्रम, श्रेणी और संयोजन, Time, Speed and Distance / समय, चाल और दूरी, Series / श्रेणी, Coding-Decoding / कूट लेखन एवं कूट वाचन, Non-Verbal Reasoning / अशाब्दिक तर्क, Percentage / प्रतिशत, Average / औसत, Profit, Loss and Discount / लाभ, हानि और बट्टा, Simple and Compound Interest / साधारण और चक्रवृद्धि ब्याज, Time and Work / समय और कार्य, Solid Mensuration / घन क्षेत्रमिति, Age Problems / आयु संबंधी प्रश्न, Arithmetic / अंकगणित, Simplification, Indices and Surds / सरलीकरण, घातांक और करणी, Algebra / बीजगणित, Probability / प्रायिकता, Trigonometry / त्रिकोणमिति, Syllogisms / न्यायवाक्य, Seating Arrangement and Puzzles / बैठक व्यवस्था एवं पहेलियाँ, Blood Relations / रक्त संबंध, Direction and Distance / दिशा एवं दूरी, Analytical Reasoning (Counting Figures Reasoning) / विश्लेषणात्मक तर्क (आकृति गणना तर्क), Mathematical Operations and Missing Numbers / गणितीय संक्रियाएँ एवं लुप्त संख्या, Calendar and Clock / कैलेंडर एवं घड़ी, Clock / घड़ी, Cubes, Dice and Figure Counting / घन, पासा एवं आकृतियों की गिनती, Venn Diagrams, Syllogism and Inequalities / वेन आरेख, न्याय वाक्य एवं असमानता, Data Arrangement / आँकड़ों की व्यवस्था, Inequality / असमानता, Analogy and Classification / सादृश्यता एवं वर्गीकरण, Order and Ranking / क्रम एवं रैंकिंग, Sets, Relations, Functions and Discrete Mathematics / समुच्चय, संबंध, फलन और विविक्त गणित, Number Systems and Number Theory / संख्या पद्धति और संख्या सिद्धांत, Coordinate Geometry, Vectors and 3D Geometry / निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति, Polynomials, Equations and Complex Numbers / बहुपद, समीकरण और सम्मिश्र संख्याएँ
  7. Section 2 | General Awareness (GK + Current Affairs) / सामान्य जागरूकता (GK + समसामयिकी): Polity / राजव्यवस्था, Scientific Achievements and Research / वैज्ञानिक उपलब्धियाँ और अनुसंधान, Biology / जीव विज्ञान, State-Specific General Knowledge / राज्य विशेष सामान्य ज्ञान, Chemistry / रसायन विज्ञान, History / इतिहास, Geography / भूगोल, Indian Economy / भारतीय अर्थव्यवस्था, Environment / पर्यावरण, Current Affairs / समसामयिकी, Static General Knowledge / स्थैतिक सामान्य ज्ञान
  8. Section 3 | Computer System and Org. (CSO): Basics of COA, Floating Point Rep, Cache Memory Organization, Instr Formats & Modes, Programming the Basic Computer, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design
  9. Section 3 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, SQL, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control
  10. Section 3 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Process Synchronization
  11. Section 3 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics
  12. Section 3 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Minimum Spanning Trees, Shortest Path Algos
  13. Section 3 | Theory Of Computation & Compiler Design: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization
  14. Section 3 | Emerging Trends (AI, Societal Ethics & MS Office): Computer Fundamentals, Emerging Tech Trends, Society, Law & Ethics, MS Office Applications, Trade, Marketing and Consumer Protection / व्यापार, विपणन एवं उपभोक्ता संरक्षण, Cyber Safety and Security, Computer Software, Operating System, Computer Networks, Word Processing (MS Word), Terms & Abbreviations, Presentation Software (MS PowerPoint), Internet of Things, Cloud Computing
  15. Section 3 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Maintenance and Configuration Management, Software Testing
  16. Section 3 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Section 3 | OOPS, C++, JAVA, HTML: OOPS with C++, Java, HTML Basics, CSS
  18. Section 3 | Java: Java Fundamentals, Array, String, IO & References, OOPS with Java
  19. Section 3 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  20. Section 3 | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  21. Section 3 | Multimedia: Multimedia
  22. BPSC Previous Year Papers:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a comprehensive lesson on finding the Least Common Multiple (LCM) and Highest Common Factor (HCF) of polynomials. The lecture begins by defining LCM as the smallest polynomial divisible by all given polynomials and demonstrates its calculation through factoring, using examples like P(x) = x² - 9 and Q(x) = x² - 3x. The video then introduces the relationship between HCF and LCM, presenting the formula HCF × LCM = Product of the given polynomials, and illustrates this with a worked example. A section on 'Shortcut Tricks' is provided, including rules for determining HCF based on degree, common factors, and division. The video concludes with a practice question asking for the HCF of x² - 9 and x² - 3x, reinforcing the concepts taught.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide, "What is LCM of Polynomials?". It defines LCM as the smallest polynomial that can be divided by all given polynomials. Two examples are shown. Example 1 factors P(x) = x² - 9 as (x-3)(x+3) and Q(x) = x² - 3x as x(x-3). The LCM is determined by taking the highest power of each unique factor, resulting in LCM = x(x-3)(x+3). Example 2 follows a similar process for P(x) = x² - 5x + 6 and Q(x) = x² - 3x, yielding LCM = x(x-2)(x-3).

  2. 2:00 – 5:00 02:00-05:00

    The video transitions to a comparison between the numeric and polynomial methods for finding HCF. It shows the Euclidean algorithm for numbers 48 and 18, where the HCF is found to be 6. This is contrasted with the polynomial method for P(x) = x³ - 3x² + 2x and Q(x) = x² - 2x + 1, where the HCF is found to be (x-1). The instructor then draws a diagram to illustrate the relationship between the factors of the polynomials, showing how the HCF is the common part and the LCM is the product of all unique factors.

  3. 5:00 – 10:00 05:00-10:00

    The instructor uses a diagram to explain the relationship between the factors of the polynomials. He writes the factors of P(x) = x² - 9 as (x-3) and (x+3), and the factors of Q(x) = x² - 3x as x and (x-3). He then shows that the HCF is the common factor (x-3), and the LCM is the product of all unique factors: x(x-3)(x+3). He also demonstrates the relationship between the HCF and LCM using the formula HCF × LCM = Product of the given polynomials, using the example of 20 and 30 to illustrate the concept.

  4. 10:00 – 12:50 10:00-12:50

    The video presents a slide titled "Relation Between HCF and LCM" with the formula: HCF × LCM = Product of the given polynomials. An example is worked out using P(x) = x² - 9 and Q(x) = x² - 3x, showing that HCF = (x-3) and LCM = x(x-3)(x+3). The instructor verifies the formula by multiplying HCF and LCM to get the product of the polynomials. The final section, "Shortcut Tricks," lists five rules: 1) HCF cannot have a degree greater than the smallest polynomial, 2) check for common factors like (x+a) or (x-b), 3) use the formula LCM = (Product / HCF), 4) if one polynomial divides the other, the smaller is the HCF and the larger is the LCM, and 5) always verify the answer using HCF × LCM = Product. The video ends with a practice question: "Find the HCF of x² - 9 and x² - 3x."

The video systematically teaches the concepts of LCM and HCF for polynomials. It starts with a clear definition and two worked examples to demonstrate the factoring method. It then draws a powerful analogy to the numeric method, using the Euclidean algorithm to show the parallel process. The core of the lesson is the relationship between HCF and LCM, which is presented as a fundamental formula. This is reinforced with a detailed example and a set of practical shortcut tricks that provide students with efficient problem-solving strategies. The progression from definition to method to formula to shortcuts creates a logical and comprehensive learning path.

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