What is factor in algebraic expression

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Before we discuss about the factors of algebraic expressions let us recall the concept of factors and multiples. If we multiply 2, 3, 5 we get 30, i.e., 30 = 2 × 3 × 5. Here, 2, 3, 5 are the factors of 30.

So to find the factors of given numbers, we express it as the product of two or more numbers. Similarly, we can find the factors of algebraic expressions.

Factors of Algebraic Expressions:  If algebraic expressions is expressed as the product of numbers, algebraic variables or  algebraic expressions, then each of these numbers and  expressions is called the factor of algebraic expressions.

Factors of the Monomials: 

It consists of every variable, their product and the number that divides it exactly.

1. Write all the possible factors of 7mn2

Solution:

The possible factors of 7 are 1, 7.

The possible factors of mn2 are m, n, n2, mn, mn2.

Therefore, all the possible factors of 7mn2 are m, n, n2, mn, mn2, 1, 7, 7m, 7n, 7n2, 7mn and 7mn2.

2. Write down all the factors of 3x2y.

Solution:

The possible factors of 3 are 1, 3.

The possible factors of x2y are x, y, xy, x2, x2y.

Therefore, all possible factors of 3x2y are x, y, xy, x2, x2y, 1, 3, 3x, 3y, 3xy, 3x2, 3x2y.

Highest Common Factor (HCF) of Monomials: 

The H.C.F. of two or more monomials is the product of the H.C.F. of the numerical coefficients and the common variables with least powers.

1. Find the H.C.F. of 2m3n2, 10m2n3, 8mn4.

Solution:

The H.C.F. of 2, 10 and 8 is 2.

The common variables appearing are m and n.

The smallest power of m appearing in 3 monomials = 1

The smallest power of n appearing in 3 monomials = 2

Therefore, monomials of common variables with the smallest power = mn2

Therefore, H.C.F. of 2m3n2, 10m2n3, 8mn4 is 2mn2.

8th Grade Math Practice

From Factors of Algebraic Expressions to HOME PAGE

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

Share this page: What’s this?

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?

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

To learn more about algebraic expressions and related concepts, visit www.byjus.com and also, download BYJU’S – The Learning App to get interactive videos of all the important maths concepts.

An algebraic expression is made up of terms. A term can be a constant or a variable, or variables with coefficients.

A factor in an expression is something that is multiplied by something else. It can be a number, variable, term or any other longer expression. For example, the factors of 2xy are 2, x and y.

A coefficient is a numerical value that is multiplied by a variable. For example, the coefficient of 7x is 7.

In an expression 5x+8y, the coefficients are 5 and 8, and the terms are 5x and 8y.

A constant is a numerical value that should not change its value. For example, in the expression 2x+6, 6 is a constant.

Algebraic expressions are combinations of variables , numbers, and at least one arithmetic operation.

For example, 2 x + 4 y − 9 is an algebraic expression.

               

What is factor in algebraic expression

Term: Each expression is made up of terms. A term can be a signed number, a variable, or a constant multiplied by a variable or variables.

Factor: Something which is multiplied by something else. A factor can be a number, variable, term, or a longer expression. For example, the expression 7 x ( y + 3 ) has three factors: 7 , x , and ( y + 3 ) .

Coefficient: The numerical factor of a multiplication expression that contains a variable. Consider the expression in the figure above, 2 x + 4 y − 9 . In the first term, 2 x , the coefficient is 2 : in the second term, 4 y , the coefficient is 4 .

Constant: A number that cannot change its value. In the expression 2 x + 4 y − 9 , the term 9 is a constant.

Like Terms: Terms that contain the same variables such as 2 m , 6 m or 3 x y and 7 x y . If an expression has more than one constant terms, those are also like terms.

Expression

Word Phrases

n + 5

Sum of a number and 5

m − 7

Difference of a number and 7

6 x

Product of 6 and a number

y ÷ 9

Quotient of a number and 9

Example:

Identify the terms, like terms, coefficients, and constants in the expression.

9 m − 5 n + 2 + m − 7

First, we can rewrite the subtractions as additions.

9 m − 5 n + 2 + m − 7 = 9 m + ( − 5 n ) + 2 + m + ( − 7 )

So, the terms are 9 m , ( − 5 n ) , m , 2 , and ( − 7 ) .

Like terms are terms that contain the same variables.

9 m and 9 m are a pair of like terms . The constant terms 2 and − 7 are also like terms.

Coefficients are the numerical parts of a term that contains a variable.

So, here the coefficients are 9 , ( − 5 ) , and 1 . ( 1 is the coefficient of the term m .)

The constant terms are the terms with no variables, in this case 2 and − 7 .

Algebraic expressions must be written and interpreted carefully. The algebraic expression 5 ( x + 9 ) is not equivalent to the algebraic expression, 5 x + 9 .

See the difference between the two expressions in the table below.

Word Phrases Algebraic Expression
Five times the sum of a number and nine

5 ( x + 9 )

Nine more than five times a number

5 x + 9

In writing expressions for unknown quantities, we often use standard formulas. For example, the algebraic expression for "the distance if the rate is 50 miles per hour and the time is T hours" is D = 50 T (using the formula D = R T ).

An expression like x n is called a power. Here x is the base, and n is the exponent. The exponent is the number of times the base is used as a factor. The word phrase for this expression is " x to the n th power."

Here are some of the examples of using exponents.

Word Phrases Algebraic Expression
Seven times m to the fourth power

7 m 4

The sum of x squared and 12 times of y

x 2 + 12 y

x cubed times y to the sixth power

x 3 ⋅ y 6