Expression: Term, Factor And Coefficient

An algebraic expression is a mathematical phrase that contains integral or fractional constants (numbers), variables (alphabets) and algebraic operators (such as addition, subtraction, division, multiplication, etc.) operating on them. These expressions are expressed in the form of terms, factors and coefficients. a + 1, a + b, x² + y, 5x/2, etc. are few examples of the algebraic expressions. The algebraic expressions are readily used as a number of mathematical formulas and find usage in generalizing them. In this article, we are going to discuss the definition of terms, factors, variables, what is a coefficient in Maths with many examples.

Table of Contents:

• What is Meant by Expression?
• What is a Term?
• Factors in an Expression
• What is a Coefficient?
• Examples
• Practice Problems
• FAQs

What is Meant by Expression?

In Mathematics, an algebraic expression is an expression that is made up of variables, constants, coefficients, and arithmetic operations. These are the different parts of the algebraic expression. 

Let us consider an expression, 2x+4y-9 

Here, the parts of the expression are:

• Coefficients are 2 and 4
• Constant is 9
• Variables are x and y
• Terms are 2x, 4y and y
• Mathematical operators used are plus (+) and minus (-).

Now, let us discuss the terms, factors and what is a coefficient in an algebraic expression in detail.

What are Terms in an Expression?

A term can be a number, a variable, product of two or more variables or product of a number and a variable. An algebraic expression is formed by a single term or by a group of terms. For example, in the expression 4x + y, the two terms are 4x and y.

It is to be noted here that terms add up to form the expression. Say there is a term 8xy, which is the product of 8, x and y. There is another term -4z, which is the product of -4 and z. On adding them up, 8xy + (-4z), we get 8xy – 4z, which is an algebraic expression. Based on the variables and their powers in terms, they can be classified into like and unlike algebraic terms of the expression.

What are the Factors of a Term?

• The numbers or variables that are multiplied to form a term are called its factors. For example, 5xy is a term with factors 5, x and y.
• The factors cannot be further factorized. For example, 5xy cannot be written as the product of factors 5 and xy. This is because xy can be factorized to x and y.
• The factors of the term 3a⁴ are 3, a, a, a and a.
• 1 is not taken as a separate factor.

What is a Coefficient in an Expression?

A coefficient is an integer that is written along with a variable or it is multiplied by the variable.  In other words, a coefficient is the numerical factor of a term containing constant and variables. For example, in the term 2x, 2 is the coefficient.

The variables which do not carry any number along with them, have a coefficient of 1. For example, the term y has a coefficient of 1. For example, in the expression 5ab, 5 is the coefficient.

More examples on Coefficients:

• -5 is the coefficient of the term –5ab².
• When there is no numerical factor in a term, its coefficient is taken as +1. For example, in the term x²y³, the coefficient is +1.
• In the term –x, the coefficient is -1.

However, all these parts of an algebraic expression are connected with each other by arithmetic operations such as addition, subtraction, or multiplication in general. Thus, these operators play a significant role in forming expressions in algebra. Even the single term can be expressed as a sum of two terms. For example, 5x can also be written as 5x + 0 or 5x – 0. But this way of representation is not actually required except to define the expression as it is a combination of all those elements (i.e. terms, variables, operators, coefficients, and constants).

Solved Examples

Example 1:

Determine the variables, terms, constants and coefficients of the algebraic expression 9x+2y-3.

Solution:

Given algebraic expression: 9x+2y-3

Here, 

Variables: x and y

Terms: 9x, 2y and 3

Constant: 3

Coefficient: 9 and 2.

Example 2: 

Find the factors of the algebraic expression 5x (2-y)

Solution:

Given expression 5x (2-y)

The factors of 5x (2-y) are 5, x, and (2-y).

Practice Questions

Identify the terms, coefficients and variables in each of the following expressions.

1. 22x² – 6x + 17
2. xy + 2x³ – 14x
3. 3p + 16
4. 15y² – 19 + 3xy + 4x – y

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