Mathematics 9th Punjab Textbook Exercise 4.1 Question 2 and 3

Описание: 📘 Class 9 Mathematics | Unit 4 (Algebraic Expressions)
🔹 Exercise 4.1 | Question 3 & 4
Factorization by Common Factor & Splitting Middle Term
Punjab Board | New Math Book 2025 | PCTB | SNC
In this video, I have explained Unit No. 4 (Algebraic Expressions), Exercise 4.1 – Question No. 1 and 2 from the New Mathematics Book for Class 9, strictly according to the Punjab Curriculum & Textbook Board (PCTB) and Single National Curriculum (SNC 2025).
This lecture is specially prepared for Class 9 Punjab Board students to understand the basic and important concept of Factorization, which plays a vital role in algebra, equations, and future chapters.

🎯 Purpose of This Video
Factorization is one of the most important and scoring topics in 9th class Mathematics. Many students face difficulty while solving:
• Common factor questions
• Three-term factorization
• Questions involving square term, x-term, and constant term
This video solves Exercise 4.1 Question 1 & 2 in a very easy, step-by-step, and exam-oriented way, so that students can attempt these questions confidently in board exams.

✅ What You Will Learn in This Video
• What is Factorization
• Why factorization is important in algebra
• Factorization by identifying common factor
• Factorization of three-term expressions
• Method of multiplying first and last term
• How to split the middle term
• Solved questions from Exercise 4.1 (Q1 & Q2)
• Common mistakes students make
• Important Punjab Board exam tips
📌 Introduction to Unit 4 (Algebraic Expressions)
In Unit 4, we study algebraic expressions and different methods to factorize them.
Factorization means writing an expression as a product of its factors.
Example:
x² + 5x = x(x + 5)
This unit builds the foundation for: ✔ Quadratic equations
✔ Algebraic fractions
✔ Advanced algebra in higher classes
📌 What is Factorization?
Factorization is the process of breaking an algebraic expression into simpler expressions that when multiplied give the original expression.
It is the reverse process of expansion.
📌 Factorization by Identifying Common Factor
(Main part of Exercise 4.1 Question 1)
In this method, we:
1️⃣ Observe all terms carefully
2️⃣ Identify the common numerical factor
3️⃣ Identify the common variable factor
4️⃣ Take the common part outside the bracket
Example:
3x + 6
= 3(x + 2)
This method is very important and frequently asked in Punjab Board papers.
📌 Factorization of Three-Term Expressions
(Exercise 4.1 Question 2)
A three-term algebraic expression usually has:
• One square term (x²)
• One linear term (x)
• One constant term
Example:
x² + 7x + 10
📌 Method: Multiply First and Last Term
(Splitting the Middle Term Method)
This is one of the most important methods for factorizing three-term expressions.
Steps:
1️⃣ Multiply first term and last term
2️⃣ Find two numbers whose: • Product = first × last
• Sum = middle term coefficient
3️⃣ Split the middle term
4️⃣ Take common factors
5️⃣ Write final factorized form
Example:
x² + 7x + 10
First × Last = 1 × 10 = 10
Middle term = 7x
Numbers: 5 and 2
x² + 5x + 2x + 10
x(x + 5) + 2(x + 5)
(x + 5)(x + 2)
📘 Exercise 4.1 – Question 1 & 2 (Punjab Board)
In this video, I have solved:
✔ Question 1 – Factorization by common factor
✔ Question 2 – Factorization of three-term expressions
✔ Step-by-step solutions
✔ Board exam style presentation
All questions are solved according to Punjab Board marking scheme.


📝 Common Mistakes Students Make
❌ Ignoring common factor
❌ Wrong splitting of middle term
❌ Sign mistakes (+ / −)
❌ Incomplete factorization


This video helps you avoid these mistakes.
🧠 Important Exam Tips
✔ Always check for common factor first
✔ Multiply first and last term carefully
✔ Verify factors by multiplication
✔ Write steps neatly in exams
✔ Practice similar questions


🏫 Boards Covered
BISE Lahore
BISE Gujranwala
BISE Rawalpindi
BISE Faisalabad
BISE Multan
BISE Sargodha
BISE Sahiwal
BISE DG Khan
BISE Bahawalpur


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