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…….
Write the coefficient of 'a' in each of the following:
(i) 5a
(ii) 5/2ab^{2}(iii) a
(iv) a
(v) 9abc
(vi) 7ax
Solution:
(i) 5a
The coefficient of a is 5
(ii) 5/2ab^{2}(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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