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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