115 LearnersLast updated on July 9th, 2025
Expression: Term, Factor, and Coefficient
Algebraic expressions contain constants and variables often connected by operations like addition, subtraction, multiplication, or division. Constants are numerical values that do not change, while variables can change.
What is an Expression?
To represent mathematical statements in a compact form, we use algebraic expressions. The expression has different parts, such as terms, factors, and coefficients. A term is part of an expression separated by mathematical operations and consists of variables, constants, or their product. Different components of a term are factors, and the symbols or letters are variables.
For example, 5x2 + 6x - 3
Terms: 5x2, 6x, and -3
Variables: x2 and x
Constants: 3
Factors: In 5x2, the factors are 5, x, and x.
In 6x, the factors are 6 and x
For -3, the factor is -3
Coefficient: Here, the coefficient of x2 is 5 and the coefficient of x is 6
What are Terms, Factors, and Coefficients of Expression?
So far, we’ve learned that different parts of an expression are named term, factor, and coefficient. In this section, we will take a look at them in detail.
Terms
The terms in an algebraic expression are parts that are separated or combined by mathematical operations. A number, variable, or even their product can be terms in any given expression. The expression is classified into monomial, binomial, and trinomial, based on the number of terms.
For example, 5x2 + 2x + 3 here, the terms are 5x2, 2x, and 3, and they are connected by addition.
Factors
Factors are those parts of a term that are multiplied together in an algebraic expression. For example, in 3xy, the factors are 3, x, and y.
Coefficients
The numbers that are multiplied by variables in an algebraic expression are called coefficients.
Real-world Applications of Expression: Term, Factor, and Coefficient
Terms, factors, and coefficients are used in algebraic expressions which are in turn used in various fields to solve different types of problems. Here are some applications showing how terms, factors, and coefficients are used in real life.
- In financial modeling and budgeting, we use terms, factors, and coefficients to calculate costs, profits, or investments. For example, in business and economics, we may use an equation like A = 100x + 300 where 100x represents the variable cost per unit and 300 is the constant.
- The algebraic expressions are used in physics to model motion, forces, or energy. For example, the kinetic energy term is ½ mv2 where ½ mv2 is the term, ½ is the coefficient, and ½, m, v and, v are factors.
- To model population or resource use, we use the algebraic expression in environmental science.
Common Mistakes and How to Avoid Them in Expression: Term, Factor, and Coefficient
Algebraic expressions are an essential part of mathematics, and students often confuse them with terms, factors, and coefficients. This is a common mistake that can be avoided. Here are some other common mistakes for you to avoid:
Mistake 1
Thinking that the whole expression is the term
One of the common mistakes students tend to make is that they treat a whole expression as a single term. For example, assuming 3x - 2y as a single term, which is wrong as it has 2 terms. Terms are parts of an expression separated by signs like + or -.
Mistake 2
Not considering the negative sign
When identifying the coefficient of a term, students frequently ignore the negative sign, for example, -5x, coefficient is -5 instead of 5. So, remember to include the sign in the numerical part when identifying the coefficient.
Mistake 3
Misidentifying constant as a variable
Some students get confused between constants and variables. For example, in the expression 5x + 3, students may wrongly identify 3 as a variable. Remember that variables are accompanied by symbols or letters, and constants are just numbers.
Mistake 4
Ignoring coefficients of 1 or -1
Students consider the terms such as x2 and -x2 to have 0 as coefficients instead of 1 and -1. So, always recognize the implied coefficient in front of the variables. For example, -x2 = -1 × x2, x3 = 1 × x3.
Mistake 5
Confusing factors with terms
Confusing factors with terms is common among students, for example, thinking 6xy as a factor instead of 6, x, and y. To avoid this confusion, remember that the factors involve multiplication, not addition or subtraction.
Solved Examples of Expression: Term, Factor, and Coefficient
Problem 1
Write the algebraic expression for the given statement: Lily has 3 apples fewer than twice the number Ben has.
2b - 3
Explanation
Let b be the number of apples Ben has
So to find twice the number of apples, multiply 2 by b.
Lily has 3 apples fewer than twice the number of Ben’s apples, i.e., 2b - 3 if written as an expression.
Therefore, the number of apples Lily has is 2b - 3.
Problem 2
Identify the terms, factors, and coefficients in 4x square - 7x + 10
Terms: 4x2 -7x, 10
Explanation
Factors: For 4x2: 4, x, and x
For -7x: -7 and x
For 10: 10
Coefficient of x2: 4
Coefficient of x: -7
Constant: 10
The term is the part of an expression that is separated by + or -. Each of the terms can be broken down into factors, and the coefficients are the numbers that are multiplied by the variable.
Problem 3
Identify the term, factor, and coefficient in 6a square b
Terms: 6a2b
Factors: For 6a2b: 6, a, a, and b
Coefficient of a2b: 6
Explanation
The term 6a2b has factors multiplied together. The factors are the coefficient 6 and variables, a2 and b.
Problem 4
Write an algebraic expression to represent her total cost: Sarah rents a bike for a flat fee of $20 and pays $3 for each additional hour she uses it.
20 + 3h
Explanation
Let h be the number of extra hours
Flat fee is $20
Extra charges are $3 per hour, so 3h
So, the total cost is 20 + 3h
Problem 5
Identify the term, factor, and coefficient in x cube + 5x square + 5x + 1
The terms are: x3, 5x2, 5x, 1
The factors of x3 are xxx
The factors of 5x2 are 5, x, and x
5 and x are the factors of 5x
The coefficient of x3 is 1
The coefficient of 5x2 is 5
The coefficient of 5x is 5
Explanation
Terms are parts in algebraic expressions that are separated by signs like + or -. Each term comprises factors, and coefficients are the numerical values multiplied by the variables.
FAQs on Expression: Term, Factor, and Coefficient
1.What is an algebraic expression?
2.What is a term in an expression?
3.What is the coefficient in 5x square y?
4.What is a constant?
5.What are the factors in 5x square?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Expression: Term, Factor, and Coefficient ?
8.How do technology and digital tools in India support learning Algebra and Expression: Term, Factor, and Coefficient ?
9.Does learning Algebra support future career opportunities for students in India?
Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
