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📘 Class 9 Maths Chapter 2 – Polynomials | Full Chapter Summary
In this chapter "Polynomials", we explore algebraic expressions in detail — their definitions, types, degrees, operations, and theorems. This chapter is crucial for building a strong algebra foundation for higher classes.


🔹 1. Introduction to Polynomials

Algebraic Expression: Combination of variables, constants, and operations (+, −, ×, ÷).

Polynomial: An algebraic expression where powers of variables are whole numbers and coefficients are real numbers.

🔹 2. Terms Related to Polynomials

Term: Each part of a polynomial separated by ‘+’ or ‘−’.

Coefficient: Numerical factor of a term.

Degree of Polynomial: The highest power of the variable.

🔹 3. Types of Polynomials (Based on Degree)

Zero Polynomial: Degree not defined (all coefficients zero).

Constant Polynomial: Degree = 0.

Linear Polynomial: Degree = 1.

Quadratic Polynomial: Degree = 2.

Cubic Polynomial: Degree = 3.


🔹 4. Types of Polynomials (Based on Number of Terms)

Monomial: 1 term (e.g., 5x).

Binomial: 2 terms (e.g., x + 3).

Trinomial: 3 terms (e.g., x² + 2x + 1).


🔹 5. Zeros of a Polynomial

Zero (Root): The value of x for which the polynomial becomes zero.

Example: For p(x) = x² − 4, zeros are ±2.


🔹 6. Remainder Theorem

If p(x) is divided by (x − a), the remainder = p(a).


🔹 7. Factor Theorem

If p(a) = 0, then (x − a) is a factor of p(x), and vice versa.


🔹 8. Factorization of Polynomials

Splitting the middle term (for quadratic polynomials).

Using Factor Theorem.

Grouping method.


🔹 9. Identities

Important algebraic identities:

(x + y)² = x² + 2xy + y²

(x − y)² = x² − 2xy + y²

(x + a)(x + b) = x² + (a + b)x + ab

x² − y² = (x − y)(x + y)

(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx


🎯 Key Learning Outcomes

Understanding polynomial structure and classification.

Finding zeros of a polynomial.

Applying remainder and factor theorem in problem-solving.

Using algebraic identities for simplification and factorization.


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