Class 10 Maths Chapter 5 Exercise 5.2 Solutions 2026 – Algebraic Fractions Notes PDF

Unit 5: Algebraic Fractions | Exercise 5.2 | Punjab Board New Syllabus 2026–27

Updated August 2026: Exercise 5.2 solutions for Algebraic Fractions have been uploaded below and are free to view or download, fully solved according to the new PCTB/PECTAA Class 10 Mathematics syllabus.

The Building Blocks for Combining Fractions

Before two algebraic fractions can be added or divided later in this chapter, it helps to know their HCF (highest common factor) and LCM (least common multiple) — exactly the same ideas used with ordinary numbers, just applied to polynomials. Exercise 5.2 teaches how to find both using factorization.

Key Concepts Covered in Exercise 5.2

HCF of Polynomials

The HCF of two or more polynomials is the product of all factors common to every polynomial, each raised to the lowest power it appears with. Finding it starts by factorizing each polynomial completely.

LCM of Polynomials

The LCM is the product of every factor that appears in any of the polynomials, each raised to the highest power it appears with. It is always a multiple of each original polynomial.

The Relationship Between HCF and LCM

For two polynomials, HCF × LCM equals the product of the two polynomials — the same relationship that holds for ordinary integers, and a useful way to check an answer.

Using Factorization as the Starting Point

Every HCF/LCM calculation in this exercise begins the same way: factorize each polynomial fully before comparing factors. Skipping or rushing this step is the most common source of errors.

Step-by-Step Solved Examples

Q. No. 1: Find the HCF of x² − 4 and x² + x − 2.

Factorize: x² − 4 = (x−2)(x+2)

Factorize: x²+x−2 = (x+2)(x−1)

Common factor: (x+2)

HCF = x + 2

Q. No. 2: Find the LCM of x² − 4 and x² + x − 2.

From Q. No. 1: x²−4 = (x−2)(x+2), and x²+x−2 = (x+2)(x−1)

LCM includes every distinct factor once, using the highest power seen: (x−2), (x+2), (x−1)

LCM = (x−2)(x+2)(x−1)

Q. No. 3: Verify that HCF × LCM equals the product of x² − 4 and x² + x − 2.

HCF × LCM = (x+2) × (x−2)(x+2)(x−1) = (x+2)²(x−2)(x−1)

Product of originals = (x−2)(x+2) × (x+2)(x−1) = (x+2)²(x−2)(x−1)

Both sides match ✔ verified

These three questions are representative samples. The full PDF notes uploaded on this page walk through every question of Exercise 5.2 in the same numbered, step-by-step format.

MCQs, Short Questions & Long Questions from This Exercise

Alongside the main exercise, this page’s uploaded notes are organized the way Punjab Board papers are structured, so students can practice by question type:

• MCQs: Quick questions on identifying the HCF of two simple factorized expressions
• Short Questions: Finding the HCF or LCM of two polynomials that factor directly, like Q. No. 1 and 2 above
• Long Questions: Finding both HCF and LCM together and verifying the HCF × LCM relationship

Where This Matters Beyond This Exercise

The LCM found here becomes the common denominator needed to add or subtract algebraic fractions in the exercises ahead, making this a direct prerequisite rather than a standalone topic. HCF and LCM of polynomials also appear in simplifying complex rational expressions in more advanced algebra.

Common Mistakes Students Make in Exercise 5.2

• Including a factor in the LCM more times than necessary, instead of using its highest power once
• Missing a factor that appears in only one polynomial when building the LCM
• Confusing HCF (common factors only) with LCM (every factor from every polynomial)
• Factorizing incorrectly, which throws off every subsequent step

Why This Exercise Matters for the Board Exam

HCF/LCM questions are a compact, reliable way for examiners to test factorization skills in a new context, and the HCF × LCM = product verification is a favorite way to add an extra mark to a question. Since this exercise directly feeds into fraction addition later in the chapter, it’s worth mastering rather than skimming.

Quick Links – Chapter 5: Algebraic Fractions

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Download Exercise 5.2 Notes PDF

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Frequently Asked Questions (FAQs)

Q1. Are these Exercise 5.2 notes free to download?

Yes, all notes on this page are completely free to view and download in PDF format.

Q2. Which board are these notes for?

These notes are prepared according to the Punjab Board syllabus and are useful for all Punjab boards (Lahore, Gujranwala, Multan, Sargodha, Rawalpindi, Faisalabad, DG Khan, Bahawalpur, Sahiwal) as well as the Federal Board (FBISE).

Q3. How is HCF/LCM of polynomials different from HCF/LCM of numbers?

The method is identical in spirit — factorize completely, then combine common or all factors — but with polynomials, the “factors” are algebraic expressions like (x+2) rather than prime numbers.

Q4. Does this page include MCQs and short questions too?

Yes, the uploaded notes include MCQs, short questions, and long questions related to this exercise’s topics, organized by question type to match the board paper pattern.

Q5. How can I download the PDF?

Click the “Download PDF” button above and the notes will open or download directly to your device.

Q6. Are these notes updated for the new 2026–27 syllabus?

Yes, these notes are prepared strictly according to the latest PCTB/PECTAA syllabus for the 2026–27 academic session.

Comments & Feedback

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