In an algebraic expression, we may find the following three parts.
(i) Terms
(ii) Factors
(iii) Coefficients
What is term ?
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.
What is 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
What is constant ?
A number which is not having any variable with it is known as constant.
Example 1 :
Identify the parts of the following expression
2x + 3
Solution :
In the expression 2x + 3 the term 2x is made of 2 factors and 2 and x while 3 is a single factor.
Example 2 :
Identify the parts of the following expression
3ab  5a
Solution :
Example 3 :
Identify the number of terms and coefficient of each term in the expression.
x^{2}y^{2}  5x^{2}y + (3/5)xy^{2}  11
Solution :
In the given expression, we have four terms.
Term 1 ==> x^{2}y^{2}
Term 2 ==> 5x^{2}y
Term 3 ==> (3/5)xy^{2}
Term 4 ==> 11
Coefficient of 1^{st} term = 1
Coefficient of 2^{nd} term = 5
Coefficient of 3^{rd} term = 3/5
Since the last term is not having any variable, it is a constant term.
Example 4 :
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 5 :
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 6 :
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 7 :
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.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Sep 16, 24 11:07 AM
Sep 16, 24 09:42 AM
Sep 14, 24 05:55 AM