CBSE Notes Class 9 Maths Chapter 2 - Introduction to Linear Polynomials
CBSE Class 9 Maths Notes Chapter 2 - Introduction to Linear Polynomials are based on the latest CBSE syllabus 2026-7 and the revised NCERT textbook, Ganita Manjari. They help students understand important concepts in a simple and structured manner, making it easier to revise key topics, definitions, solved examples, and important points before class tests and annual examinations.
The Chapter "Introduction to Linear Polynomials" introduces students to the basic concepts of algebraic expressions and polynomials. Students learn about variables, constants, terms, coefficients, polynomials, degree, and different types of polynomials. The chapter further covers linear polynomials, zeroes of polynomials, linear growth and decay, linear equations in two variables, their solutions, graphs, straight lines, and the slope-intercept form. These concepts help students develop algebraic reasoning, understand relationships between variables, and interpret mathematical information graphically, providing a strong foundation for higher-level algebra and coordinate geometry.
1.0Download CBSE Notes Class 9 Maths Chapter 2 - Introduction to Linear Polynomials Notes
Download CBSE Class 9 Maths Chapter 2 – Introduction to Linear Polynomials Notes to understand key concepts such as polynomials, linear polynomials, zeroes, and linear equations. These notes provide concise explanations and important concepts for quick revision, homework, practice, and exam preparation.
2.0Important Concepts Class 9 Maths Chapter 2 - Introduction to Linear Polynomials
Algebraic Expression
An algebraic expression is a combination of constants and variables connected by operations such as addition, subtraction, multiplication, and division.
Variable and Constant
Variable: A quantity that can have different numerical values, such as x, y, and a.
Constant: A quantity with a fixed value, such as 3, 5, 8, or –11.
Terms and Coefficients
Terms: Parts of an expression separated by + or – signs.
Coefficient: A factor of a term.
Numerical coefficient: The numerical factor of a term.
Constant term: A term without a variable factor.
Like and Unlike Terms
Like terms: Terms having the same variables with the same powers.
Unlike terms: Terms having different variables or powers.
Polynomial
A polynomial is an algebraic expression in which the powers of the variables are non-negative integers.
For example, 3x² – 4x + 5 is a polynomial.
Degree of a Polynomial
The degree of a polynomial in one variable is the highest power of the variable.
Example: The degree of 3x⁷ – 4x⁶ + x + 9 is 7.
Types of Polynomials by Degree
Polynomials by Number of Terms
Monomial: One term, such as 2x.
Binomial: Two unlike terms, such as 2x + 1.
Trinomial: Three unlike terms, such as x² + x + 6.
Value and Zero of a Polynomial
The value of a polynomial is found by putting a given value of the variable in the polynomial.
A real number a is a zero of a polynomial f(x) if f(a) = 0.
Linear Growth and Decay
Linear growth: Represents a steady increase and can be written as mx + b.
Linear decay: Represents a steady decrease and can be written as –mx + b.
Here, the rate and starting value help form the expression.
Linear Equation in Two Variables
A linear equation in two variables can be written as:
ax + by + c = 0
Here, a, b, and c are real numbers, and a and b are not zero together. A linear equation in two variables has infinitely many solutions.
Graph of a Linear Equation
The graph of a linear equation in two variables is a straight line. To draw it:
Write the equation in a suitable form.
Find two or three solutions.
Plot the points on the graph.
Join the plotted points to form a straight line.
Slope-Intercept Form
The equation of a line in slope-intercept form is:
y = mx + c
Here:
m = slope of the line
c = y-intercept
The slope of a line through (x₁, y₁) and (x₂, y₂) is:
m = (y₂ − y₁)/(x₂ − x₁)
3.0Other Study Materials for Class 9 Maths
Students can use additional study materials along with these notes, such as:
4.0Why CBSE Notes Class 9 Maths - Introduction to Linear Polynomials
These notes help students revise Chapter 2 and understand the basic ideas of algebra. They are useful when studying the chapter and solving questions.
- Quick revision: Read the main points before a test.
- Easy to follow: Learn each topic one by one.
- Question practice: Check the notes while working on exercises.
- Test preparation: Revise important topics before school tests and exams.
- Strong basics: Understand the chapter well before moving to other Maths topics.