NCERT Class 10 Mathematics Mathematics: Chapter 2 — POLYNOMIALS
This chapter, NCERT Class 10 Mathematics Chapter 10: Polynomials, introduces students to the concept of polynomials in one variable and their degrees. It revisits linear, quadratic, and cubic polynomials, defining their general forms (ax+b, ax^2+bx+c, ax^3+bx^2+cx+d) and providing examples. The chapter explains the value of a polynomial at a given point and defines zeroes of a polynomial as the real numbers k for which p(k)=0. It highlights the relationship between the zero of a linear polynomial and its coefficients. The text also poses questions about the relationship between zeroes and coefficients of other polynomial types and introduces the division algorithm for polynomials. Finally, it touches upon the geometrical meaning of zeroes by considering the graphical representations of polynomials, preparing students for further exploration in CBSE mathematics.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 10 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 2 — POLYNOMIALS |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 4 minutes |
| Word count | 777 |
Learning outcomes
- Define and identify polynomials of different degrees (linear, quadratic, cubic).
- Understand the concept of the value of a polynomial at a point.
- Define and find the zeroes of a polynomial.
- Relate the zero of a linear polynomial to its coefficients.
- Understand the geometrical interpretation of polynomial zeroes.
Vocabulary
| Word | Meaning |
|---|---|
| Polynomial | An expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. |
| Degree of a polynomial | The highest power of the variable in a polynomial. |
| Linear polynomial | A polynomial of degree 1. |
| Quadratic polynomial | A polynomial of degree 2. |
| Cubic polynomial | A polynomial of degree 3. |
| Zero of a polynomial | A real number k such that p(k) = 0. |
| Value of a polynomial | The value obtained by substituting a real number for the variable in a polynomial. |
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Practice questions
- What is the degree of the polynomial 7u^6 – 4u^2 + 8u + 2? Answer: 6
- Give an example of a quadratic polynomial. Answer: For example, 2x^2 + 3x – 5.
- What is the zero of the linear polynomial 2x + 3? Answer: -3/2
- If p(x) = x^2 – 3x – 4, find p(0). Answer: -4
Frequently asked questions
What is a polynomial?
A polynomial is an algebraic expression with variables, coefficients, and non-negative integer exponents, using operations like addition, subtraction, and multiplication.
What is the degree of a polynomial?
The degree of a polynomial is the highest power of the variable present in the polynomial.
What are the types of polynomials based on degree?
Based on degree, polynomials are classified as linear (degree 1), quadratic (degree 2), and cubic (degree 3), among others.
What does it mean for a number to be a zero of a polynomial?
A real number k is a zero of a polynomial p(x) if substituting k for x results in p(k) = 0.
How do you find the zero of a linear polynomial ax + b?
The zero of a linear polynomial ax + b is found by solving ax + b = 0, which gives x = -b/a.
What is the value of a polynomial?
The value of a polynomial p(x) at a real number k is the value obtained by replacing x with k, denoted as p(k).
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NCERT Class 10 Mathematics — Mathematics — Chapter 2 — POLYNOMIALS. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.