Class 10 CBSE Maths Chapter 2: Polynomials – Full Notes with Formulas & Examples

  Understanding polynomials is a key part of Class 10 Mathematics. This chapter lays the foundation for many algebraic concepts used in higher classes. In this post, you will find easy explanations, formulas, and a PDF download link of notes that will help you prepare well for your exams.

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✍️ What is a Polynomial?

A polynomial is an algebraic expression that consists of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

Examples of polynomials:

• $x^2 + 2x + 3$

• $5y^3 - 4y + 7$

• $3a^2 + 2ab + b^2$

But expressions like $\frac{1}{x}$ or $\sqrt{x}$ are not polynomials.

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🧠 Types of Polynomials Based on Degree

Degree	Example	Type
0	5	Constant
1	$x + 1$	Linear Polynomial
2	$x^2 + 3x + 2$	Quadratic Polynomial
3	$x^3 - 1$	Cubic Polynomial

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📚 Important Concepts in Chapter 2

1. Zeroes of a Polynomial

• The value of the variable which makes the polynomial equal to zero.

• For example:
  If $p(x) = x^2 - 4$, then
  $p(2) = 2^2 - 4 = 0$, so 2 is a zero of the polynomial.

2. Relationship Between Zeroes and Coefficients

This is mainly used in Quadratic and Cubic polynomials.

• Quadratic Polynomial:
  For $ax^2 + bx + c$:

  • Sum of zeroes = $-\frac{b}{a}$

  • Product of zeroes = $\frac{c}{a}$

• Cubic Polynomial:
  Similar formulas apply, but more complex.

3. Division Algorithm for Polynomials

It states that:
If $p(x)$ and $g(x)$ are any two polynomials such that
degree of p(x) ≥ degree of g(x),
then there exist polynomials $q(x)$ and $r(x)$ such that:

$$p(x) = g(x) \cdot q(x) + r(x)$$

Where:

• $p(x)$ is the dividend

• $g(x)$ is the divisor

• $q(x)$ is the quotient

• $r(x)$ is the remainder

• $\text{degree of } r(x) < \text{degree of } g(x)$

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✨ Benefits of These Notes

• 🔹 Covers all important formulas

• 🔹 Suitable for both CBSE and State Board students

• 🔹 Easy-to-understand explanations

• 🔹 Neatly formatted PDF

These notes are very helpful for school exams and board preparation. Use them for quick revision and better understanding.

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📥 Download Chapter 2 Polynomials Notes PDF

Click the button below to download your notes in PDF format:

Class 10 Maths – Chapter 2: Polynomials | Notes + Practice Questions

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Final Words

Chapter 2 – Polynomials is one of the most scoring chapters in Class 10 Maths. Understanding zeroes, relationships, and the division algorithm gives you the foundation for solving many complex problems. Practice well and use the notes to revise regularly.

➡️ If you found these notes helpful, don’t forget to check out other chapters too