NCERT Solutions Class 9 Maths Chapter 2 guides you through Polynomials with detailed solutions to all 30 questions across 4 exercises. You’ll learn how to identify polynomial types, apply the Remainder and Factor Theorems to factorize expressions, use algebraic identities to simplify complex problems, and find zeros of polynomials. Each solution includes the exact steps needed for CBSE exams, with tips on spotting patterns and avoiding calculation errors that cost marks.
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All exercises with step-by-step solutions | Updated 2025-26 | Free Download
Download PDF (Free)NCERT Solutions Class 9 Maths Chapter 2 Polynomials – Complete Guide
NCERT Class 9 Chapter 2 Polynomials introduces you to one of the most important topics in algebra that forms the foundation for higher mathematics. You’ll explore what polynomials are, understand their degree and classification (linear, quadratic, cubic), and learn about polynomial expressions in one variable. This chapter carries significant weightage of 10 marks in CBSE board exams, making it essential for scoring well.
📊 CBSE Class 9 Maths Chapter 2 – Exam Weightage & Marking Scheme
| CBSE Board Marks | 10 Marks |
| Unit Name | Algebra |
| Difficulty Level | Medium |
| Importance | Very High |
| Exam Types | CBSE Board, State Boards |
| Typical Questions | 2-3 questions |
You will learn powerful techniques including polynomial division using both long division and synthetic methods. The Remainder Theorem and Factor Theorem are game-changers that you’ll master—these theorems help you find remainders without actual division and factorize complex polynomials efficiently. You’ll also discover the relationship between zeros of polynomials and their coefficients, which is frequently tested in board exams through 2-3 mark questions.
This chapter builds directly on your knowledge of algebraic expressions from Class 8 and prepares you for quadratic equations in later chapters. The factorization methods you learn here—splitting the middle term, using identities, and factor theorem—are not just exam-focused but also applicable in solving real-world problems involving area calculations, profit-loss scenarios, and optimization problems.
Quick Facts – Class 9 Chapter 2
| 📖 Chapter Number | Chapter 2 |
| 📚 Chapter Name | Polynomials |
| ✏️ Total Exercises | 4 Exercises |
| ❓ Total Questions | 30 Questions |
| 📅 Updated For | CBSE Session 2025-26 |
Expect a mix of question types: MCQs testing basic concepts, 2-mark questions on finding zeros and remainders, 3-mark problems on factorization, and 4-mark questions combining multiple concepts. With consistent practice of NCERT solutions and understanding the core theorems, you’ll find this chapter both manageable and rewarding. Master polynomials now, and you’ll have a strong algebraic foundation for Class 10 and competitive exams ahead.
NCERT Solutions Class 9 Maths Chapter 2 – All Exercises PDF Download
Download exercise-wise NCERT Solutions PDFs for offline study
| Exercise No. | Topics Covered | Download PDF |
|---|---|---|
| EXERCISE 2.1 | Complete step-by-step solutions for 5 questions | 📥 Download PDF |
| EXERCISE 2.2 | Complete step-by-step solutions for 4 questions | 📥 Download PDF |
| EXERCISE 2.3 | Complete step-by-step solutions for 5 questions | 📥 Download PDF |
| EXERCISE 2.4 | Complete step-by-step solutions for 16 questions | 📥 Download PDF |
Polynomials – Key Formulas & Concepts
Quick reference for CBSE exams
| Formula | Description | When to Use |
|---|---|---|
| Polynomial in one variable \(p(x) = a_n x^n + a_{n-1} x^{n-1} + … + a_1 x + a_0\) | General form of a polynomial where ‘x’ is the variable and ‘n’ is a non-negative integer (the degree). a_n, a_{n-1}, … a_0 are coefficients. Note: The powers of ‘x’ must be whole numbers. If you see a negative or fractional power, it’s NOT a polynomial. | Identifying if an expression is a polynomial, determining the degree of a polynomial. |
| Zero of a Polynomial \(p(a) = 0\) | A real number ‘a’ is a zero of the polynomial p(x) if substituting x = a makes the polynomial equal to zero. Note: Zeros are also called roots of the polynomial equation. A polynomial can have multiple zeros. | Finding the values of ‘x’ that make a polynomial equal to zero; solving p(x) = 0. |
| Remainder Theorem \(p(x) = q(x) \cdot g(x) + r(x)\) | If p(x) is divided by (x – a), the remainder is p(a). Note: The degree of r(x) must be less than the degree of g(x). When dividing by (x-a), r(x) is a constant. | Finding the remainder without performing long division. Useful when dividing by a linear polynomial (x – a). |
| Factor Theorem \((x – a)\) is a factor of \(p(x)\) if and only if \(p(a) = 0\) | States that if p(a) = 0, then (x – a) is a factor of p(x), and vice versa. Note: A direct application of the Remainder Theorem. If p(a) = 0, the remainder is zero, meaning (x-a) divides p(x) exactly. | Checking if (x – a) is a factor of a polynomial, factoring polynomials, finding zeros. |
| Algebraic Identity 1 \((a + b)^2 = a^2 + 2ab + b^2\) | Expansion of the square of a sum. Note: Memorize this! Common mistake: forgetting the 2ab term. | Expanding squared binomials, simplifying expressions, factoring quadratic expressions. |
| Algebraic Identity 2 \((a – b)^2 = a^2 – 2ab + b^2\) | Expansion of the square of a difference. Note: Similar to (a+b)², but with a minus sign before the 2ab term. | Expanding squared binomials, simplifying expressions, factoring quadratic expressions. |
| Algebraic Identity 3 \(a^2 – b^2 = (a + b)(a – b)\) | Difference of squares factorization. Note: Very useful for quick factorization. Look for perfect squares being subtracted. | Factoring expressions in the form a² – b², simplifying expressions, solving equations. |
| Algebraic Identity 4 \((x + a)(x + b) = x^2 + (a + b)x + ab\) | Expansion of the product of two binomials with a common term. Note: Helps in factoring quadratics that can be expressed in this form. | Expanding binomials, factoring quadratic expressions. |
| Algebraic Identity 5 \((a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca\) | Expansion of the square of a trinomial. Note: Remember all the cross terms (2ab, 2bc, 2ca). Easy to miss one. | Expanding expressions with three terms squared. |
| Algebraic Identity 6 \((a + b)^3 = a^3 + b^3 + 3a^2b + 3ab^2 = a^3 + b^3 + 3ab(a + b)\) | Expansion of the cube of a sum. Note: Both forms of the expansion are useful. Choose the one that suits the problem best. | Expanding cubed binomials. |
| Algebraic Identity 7 \((a – b)^3 = a^3 – b^3 – 3a^2b + 3ab^2 = a^3 – b^3 – 3ab(a – b)\) | Expansion of the cube of a difference. Note: Similar to (a+b)³, but pay attention to the signs. | Expanding cubed binomials. |
| Algebraic Identity 8 \(a^3 + b^3 + c^3 – 3abc = (a + b + c)(a^2 + b^2 + c^2 – ab – bc – ca)\) | Factorization of a³ + b³ + c³ – 3abc. Note: Important identity! If a + b + c = 0, then a³ + b³ + c³ = 3abc. | Factoring expressions in this specific form. |
| Special Case of Identity 8 If \(a + b + c = 0\), then \(a^3 + b^3 + c^3 = 3abc\) | Simplified form of identity 8, when the sum of the three terms is zero. Note: This is a VERY helpful shortcut. Look for problems where a + b + c = 0. | When you know a + b + c = 0, you can directly calculate a³ + b³ + c³. |
Frequently Asked Questions – NCERT Class 9 Maths Chapter 2
📚 Related Study Materials – Class 9 Maths Resources
| Resource | Access |
|---|---|
| NCERT Class 9 Mathematics Textbook | Download Book |
| NCERT Class 9 Science Solutions | View Solutions |
| RD Sharma Class 9 (Updated 2025-26) | View Solutions |
| NCERT Class 9 English (Beehive) | Download Book |