Summary - mathemtics

Class 9 Mathematics Notes: Polynomials (NCERT +
RD Sharma)

1. Introduction to Polynomials
A polynomial is an algebraic expression made up of variables and constants, combined using
addition, subtraction, and multiplication, with non-negative integer exponents only.

Examples:
• x² + 3x + 2
• 5y³ − 2y + 7
Non-examples:
• 1/x + 2
• x^(-2) + 1


2. Types of Polynomials
Based on degree:
• Constant Polynomial → degree 0
• Linear Polynomial → degree 1
• Quadratic Polynomial → degree 2
• Cubic Polynomial → degree 3

Based on terms:
• Monomial: one term
• Binomial: two terms
• Trinomial: three terms


3. Degree of a Polynomial
The degree is the highest power of the variable.

Examples:
• 7x■ + 2x² + 1 → degree 4
• 5x + 8 → degree 1


4. Zeroes of a Polynomial
A zero of a polynomial is the value of x for which polynomial becomes zero.

Example:
For p(x)=x−5,
p(5)=0, so 5 is a zero.


5. Graphical Representation
The x-coordinate where graph cuts x-axis gives zeroes.

Linear polynomial → one zero
Quadratic polynomial → at most two zeroes
Cubic polynomial → at most three zeroes