Mathematics Notes for Class 9 Polynomials

Polynomials

In this chapter, you will learn about polynomials, their types, how to add, subtract, and multiply them, and how to find their degree and zeros. By the end of this chapter, you will be able to solve problems involving polynomials and understand their importance in algebra.

Key Concepts

Polynomial: An algebraic expression made up of terms with variables and coefficients, where the variables have whole number exponents.
Degree of a Polynomial: The highest power of the variable in the polynomial.
Coefficient: The number multiplied by the variable in a term.
Constant Term: A term without any variable.

Types of Polynomials

Monomial: A polynomial with one term (e.g., 5x).
Binomial: A polynomial with two terms (e.g., x + 3).
Trinomial: A polynomial with three terms (e.g., x² + 2x + 1).
General Polynomial: May have any number of terms.

Standard Form of a Polynomial

A polynomial is written in standard form when its terms are arranged in descending order of the powers of the variable.

Example: 3x² + 2x + 5

Operations on Polynomials

Addition: Add like terms together.
Subtraction: Subtract like terms.
Multiplication: Multiply each term in one polynomial by each term in the other.

Example (Addition): (2x + 3) + (x + 5) = 3x + 8

Example (Multiplication): (x + 2)(x + 3) = x² + 5x + 6

Degree and Zeros of a Polynomial

Degree: The highest exponent of the variable.
Zero: A value of the variable that makes the polynomial equal to zero.

Example: For p(x) = x² - 4, the zeros are x = 2 and x = -2.

Practice Questions

Write the degree and constant term of the polynomial 4x³ + 2x² - x + 7.
Add: (3x + 2) and (5x - 4).
Subtract: (x² + 6x + 5) from (2x² + 3x + 1).
Multiply: (x + 2) by (x - 1).
Find the zeros of the polynomial p(x) = x² - 9.

Challenge Yourself

Write a trinomial and find its degree and coefficients.
If p(x) = x² + 5x + 6, factorize p(x) and find its zeros.

Did You Know?

Polynomials are used in computer science, physics, and engineering to solve real-world problems.
The word "polynomial" comes from Greek, meaning "many terms".

Glossary

Term: A part of a polynomial separated by + or - signs.
Coefficient: The number in front of a variable.
Degree: The highest power of the variable.
Zero: A value that makes the polynomial equal to zero.

Answers to Practice Questions

Degree: 3, Constant term: 7
3x + 2 + 5x - 4 = 8x - 2
(2x² + 3x + 1) - (x² + 6x + 5) = x² - 3x - 4
(x + 2)(x - 1) = x² + x - 2
p(x) = x² - 9 = 0 ⇒ x = 3, x = -3

Practice working with polynomials to build a strong foundation in algebra!

Mathematics Class 9 - Polynomials Notes