Terms factors and coefficients :
A single variable or a constant or a combination of these as a product or quotient forms a term.
Examples of terms :
5, a, 3ab, 21/7, ........... etc
Terms can be added or subtracted to form an expression. In the expression 2x + 3 the term 2x is made of 2 factors and 2 and x while 3 is a single factor.
Consider the expression 3ab – 5a. It has two terms 3ab and 5a. The term 3ab is a product of factors 3, a and b. The term 5a is a product of 5 and a. The coefficient of a variable is a factor or factors.
Example :
In the term 3ab;
(i) the coefficient of ab is 3 (ii) the coefficient of a is 3b
(iii) the coefficient of b is 3a.
In the term –5a the coefficient of a is –5
Example 1 :
Identify the number of terms and coefficient of each term in the expression.
x^{2} y^{2}  5 x^{2} y + (3/5) xy^{2}  11
Solution :
In the given expression, we have four terms.
Term 1 ==> x^{2} y^{2}
Term 2 ==>  5 x^{2} y
Term 3 ==> (3/5) xy^{2}
Term 4 ==> 11
Coefficient of 1st term = 1
Coefficient of 2nd term = 5
Coefficient of 3rd term = 3/5
Since the last term is not having any variable, it is a constant term.
Example 2 :
Identify the number of terms, coefficient and factors of each term in the expression.
3abc  5ca
Solution :
The given expression contains two terms.
Term 1 ==> 3abc
Term 2 ==> 5ca

Terms 
Coefficients 
Factors 
1) 
3abc 
3 
a, b and c 
2) 
5ca 
5 
c and a 
Example 3 :
Identify the number of terms, coefficient and factors of each term in the expression.
1 + x + y^{2}
Solution :
The given expression contains three terms.
Term 1 ==> 1
Term 2 ==> x
Term 2 ==> y^{2}

Terms 
Coefficients 
Factors 
1) 
1 
 
 
2) 
x 
1 
x 
3) 
y^{2} 
1 
y and y 
Example 4 :
Identify the number of terms, coefficient and factors of each term in the expression.
3x^{2} y^{2}  3xyz + z^{3 }
Solution :
The given expression contains three terms.
Term 1 ==> 3x^{2} y^{2}
Term 2 ==>  3xyz
Term 2 ==> z^{3 }

Terms 
Coefficients 
Factors 
1) 
3x^{2} y^{2} 
3 
x^{2} and y^{2} 
2) 
 3xyz 
3 
x, y and z 
3) 
z^{3 } 
1 
z, z and z 
Example 5 :
The coefficient of x^{4} in 5x^{7} + (3/7) x^{4}  3x^{3} + 7x^{2}  1
Solution :
The coefficient of x^{4 }is 3/7.
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