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166 LearnersLast updated on September 26, 2025
Expression: Term, Factor, and Coefficient
Algebraic expressions contain constants and variables often connected by operations like addition, subtraction, multiplication, or division. Constants are fixed numerical values, while variables can vary.
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. Factors are the components of a term, while symbols or letters represent 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 term in an expression can be a number, a variable, or a product of both. 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 the multiplicative components of a term.
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.
- Algebraic expressions are used in physics to model motion, forces, and energy.
For example, the kinetic energy term is ½ mv², where ½ is the coefficient and the factors are ½, m, v, and v.
- 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
Treating the entire expression as a single 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 sometimes think terms like x² and -x² have a coefficient of 0 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 4x² - 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 6a² b
Terms: 6a2b
Factors: For 6a2b: 6, a, a, and b
Coefficient of a2b: 6
Explanation
The term 6a²b consists of factors: 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
The extra charge is $3 per hour, so it is represented as 3h.
So, the total cost is 20 + 3h
Problem 5
Identify the term, factor, and coefficient in x³ + 5x² + 5x + 1
- The terms are: x3, 5x2, 5x, 1
- Factors:
The factors of x3 are x × x × x
The factors of 5x2 are 5, x, and x
5 and x are the factors of 5x
- Coefficient:
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 5x²y?
4.What is a constant?
5.What are the factors in 5x square?
6.How does learning Algebra help students in United States make better decisions in daily life?
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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.
