Coefficient of a Variable

The symbol or number appearing before a variable used in an algebraic term is called its coefficient.

For Example:

In -7ab, 7a is the coefficient of b and -7 is the coefficient of ab etc.

In -pq, -1 is coefficient of pq.

Definition of Coefficient:

Any factor or group of factors of a product is known as the coefficient of remaining factors.

For Example: 

In product 6mxy,

6 is the coefficient of mxy,

6x is the coefficient of my,

xy is the coefficient of 6m,

mxy is the coefficient of 6 and so on……. 

Note: In the term 'm', the coefficient of m is 1 since 1 times m is equal to m. Similarly, in the term '-m' the coefficient of m is -1 since -1 times m is equal to -m.

If a factor is a numerical quantity, it is called numeral coefficient of remaining factors and if the factor involves letters, it is called the literal coefficient of remaining factors.

For example:

(i) In product 11xy, we get;

11 is numerical coefficient of xy,

x is literal coefficient of 11y,

xy is literal coefficient of 11,

y is literal coefficient of 11x

11y is literal coefficient of x and so on…….

(ii) In product -7ab, we get;

-7 is numerical coefficient of ab,

a is literal coefficient of -7b,

ab is literal coefficient of -7,

b is literal coefficient of -7a

-7b is literal coefficient of a and so on…….

(iii) In product 3m²n, we get;

3 is numerical coefficient of m²n,

m² is literal coefficient of 3n,

m²n is literal coefficient of 3,

n is literal coefficient of 3m²

3n is literal coefficient of m² and so on…….

Write the coefficient of 'a' in each of the following:

(i) 5a

(ii) 5/2ab²

(iii) a

(iv) -a

(v) 9abc

(vi) -7ax

Solution:

(i) 5a

The coefficient of a is 5

(ii) 5/2ab²

The coefficient of a is 5/2b²

(iii) a

The coefficient of a is 1 [Since a = 1 ∙ a]

(iv) -a

The coefficient of a is -1 [Since -a = -1 ∙ a]

(v) 9abc

The coefficient of a is 9bc

(vi) -7ax

The coefficient of a is -7x

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