NCERT Book Class 9 Mathematics Chapter 2 Introduction to Linear Polynomials

Introduction to
2 Linear Polynomials

2.1 Introduction
We have learnt about algebraic expressions in earlier grades. In this
chapter, we will learn about the special types of algebraic expressions
called linear polynomials. Let us first consider a few examples of
algebraic expressions.
Example 1: Raju went to a shop
where there were sealed boxes of
different colours on sale. The shop
owner told him that the red boxes
have 4 pens each and the blue
boxes have 5 pencils each. Now, if
Raju bought x red boxes and y blue
boxes, how can he quickly figure
out the total quantity of pens and
pencils? Also, if he got 3 extra pens
free, how many pens and pencils did
Fig. 2.1
he get altogether?
Observe that x red boxes will have 4x pens and y blue boxes will
have 5y pencils. Also, he got 3 extra pens free. Thus, the total number
of pens and pencils is given by the algebraic expression 4x + 5y + 3.
In this example, 4x, 5y and 3 are terms of the expression, x and y are
letter-numbers, the numbers 4 and 5 are the coefficients of x and y,
respectively, and 3 is a constant. From now onwards, we will use a
widely used alternate word for letter-numbers: variables. Thus in the
expression 4x + 5y + 3, we say that the variables used are x and y.
Example 2: A rectangular garden of length l metres and width w
metres has to be fenced and decorated. A wire fence is to be laid along
the length costing `100 per metre and a wooden fence is to be built
along the width costing `80 per metre. Special seeds have to be sown
throughout the garden which will cost `50 per square metre.
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