Class 9 Mathematics • Ganita Manjari • Chapter 2
In this chapter, we learn about polynomials, their terms, coefficients, constants and degrees. We also learn about linear polynomials and how algebraic expressions can be used to describe mathematical patterns and relationships.
You will learn how to identify polynomials, find their degree and coefficients, evaluate expressions, understand linear patterns and study linear relationships.
Chapter concepts, explanations, examples and revision notes.
Important practice questions with answers and Hindi explanations for examination preparation.
Exercise 2.1 से End-of-Chapter तक सभी textbook exercises यहाँ मिलेंगी।
Click on any topic to jump directly to that topic.
A polynomial is an algebraic expression made up of one or more terms.
A polynomial is made up of terms that are added or subtracted.
The separate parts of a polynomial are called its terms.
Its terms are:
The numerical factor multiplying a variable is called its coefficient.
Coefficient of x² = 6
Coefficient of x = -4
A term without a variable is called the constant term.
Constant term = 6
The degree of a polynomial is the highest power of the variable.
Highest power = 3
Therefore, degree = 3
A non-zero constant polynomial has degree 0.
A polynomial of degree 1 is called a linear polynomial.
To find the value of a polynomial, substitute the given value of the variable.
For x = 4:
A pattern is linear when the difference between consecutive values remains constant.
Each term increases by 3.
Therefore, it is a linear pattern.
A quantity shows linear growth when it increases by a fixed amount in equal intervals.
A plant is 20 cm tall and grows 5 cm each month.
A quantity shows linear decay when it decreases by a fixed amount in equal intervals.
A linear relationship describes a constant rate of change between two quantities.
If one quantity changes by a fixed amount whenever the other quantity changes by one unit, the relationship can be linear.
A linear relationship can often be written in the form:
Here a = 3 and b = 2.
A linear relationship can be represented by a straight line on a graph.
Choose values of x, calculate y and plot the resulting points.
Always check your coordinates before drawing the line.
Linear relationships and polynomials can be useful in many practical situations.
अब chapter की exercises और important questions से practice करें।