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Expression: Term, Factor and Coefficient

A combination of constants and variables connected by the mathematical operators like +, -, ×, ÷ is known as an algebraic expression. Constants are the numbers that have a fixed numerical value and variables are the numbers that can take various numerical values. The value of an expression depends upon the values of the variables of an expression. The concept of an algebraic expression is well understood when there is a clear idea about the terms, factors, and coefficients of an algebraic expression.

1.	Definition of Expression
2.	Term, Factors, Coefficient of Expression
3.	Solved Examples
4.	Practice Questions
5.	FAQs

Definition of Expression

The mathematical statements are written in algebraic expressions. For instance, when we say c is doubled, it is expressed as 2c. 2 less than t is expressed as t-2. Here 2c and t-2 are algebraic expressions. An expression comprises the terms, factors, and coefficient. The terms are the numbers or the variables added together, factors are the numbers or the variables that are multiplied together and the coefficient is the number multiplied to the variable. In an expression 3x²+ 5x + 2, there are 3 terms: 3x², 5x and 2. The variables are x²and x. The constant is 2 and the coefficient of x²is 3 and that of x is 5. Thus an expression is a combination of terms, variables, factors, coefficients, and constants.

Expression - Term, Factor and Coefficient

Term, Factors and Coefficient of Expression

Let's understand the different parts of an expression with an example. Consider a²- 6a + 9.

Terms: a²,6a, and 9.
Variables: a², a
Constants:9
Factors: a, a are the factors of term 1, -6 and a are the factors of term 2, and 9 is the factor of term 3.
Coefficients:1 is the coefficient of a², -6 is the coefficient of a, and 9 is the coefficient of the constant term
Operators:- and +

Terms

Several parts of an algebraic expression separated by + or - signs are called the terms of the expression. The terms can be single numbers, variables, or the product of a number and variable. On the basis of the number of terms, the polynomials are classified as monomial, binomial, trinomial. Thus we get polynomials derived from the Greek words poly and nomial meaning many terms. The terms can be like terms or unlike terms.

2a²b has one term. It is monomial.
2xy - 3 has 2 terms and it is called binomial.
x² + 3x + 2 has 3 terms and is a trinomial.

Factors

Factors are part of the product. 5y denotes 5 × y where 5 and y are multiplied together to form 5y and thus both are the factors of this term 5y. Expressing the term as a product of 2 or more variables or numbers is called factorization. We might require to factorize any given algebraic expression. For example, y² + y is factorized as y(y+1), which means that y and y+1 are factors of y² + y and a²- b² = (a+b)(a-b), which means (a+b) and (a-b) are the factors of a²- b².

Coefficient

A number or a variable that is multiplied to another variable in the expression forms the coefficient. Consider 4a². In this case, 4 is the numerical coefficient of a² and a² is the literal coefficient of 4. In the term, 12n, 12 is the numerical coefficient of n. If there is no number, it is understood that 1 is the coefficient. In the expression, a²+ b, 1 is the numerical coefficient of a²and also b.

The terms that have the same literal coefficients are called the like terms, whereas the terms that have different literal coefficients are called the unlike terms.

Like Terms:3x³, -x³ , 2x³
Unlike Terms: 2x², 6x, -x⁴

Here are a few interesting articles related to expressions:

Important Notes

The mathematical statements that are expressed in words are expressed using variables in algebra and these form the algebraic expressions.
An expression is built of terms, variables, constants, factors, and coefficients with the mathematical operators + or - in between the terms.

Example 1: Write the algebraic expressions for the given statements.
a) Increase your fiber content 6 times what you eat now.
b) Bob collected 50 shells more than what Mike collected.
c) Tom's age is twice his brother's age.
Solution:
a) Let the content eaten now be the unknown variable c. Thus, 6 times what we eat is 6 times c. The required expression is 6c.
b) Let the shells collected by Mike be n. Shells collected by Bob is 50 more than n. Then the required expression is n + 50
c) Let brother's age be a. Tom's age is 2 times a. Then the required expression is 2a.
Example2: Find the expression. Marc is paid a flat of $50 per week and $5 for every extra hour.
Solution:
Let t be every extra hour worked by Marc.
The required expression is 50 + 5t
Example 3: Identify the terms and the factors using the tree diagram for the following expression: 2t³ + 9t²+ t - 12.
Solution:
The expression can be split into 4 terms and each term is split into factors.
Terms: 2t³, 9t², t, and 12.
Factors: 2, t, t, t,9, t, t, t, -1 and 12

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FAQs on Expression: Term, Factor and Coefficient

How Do You Find the Coefficient of an Expression?

A coefficient an expression is the numerical factor of the variable in a term. In 3x² + 2x, we have 2 terms. In the first term, the numerical factor is 3, and 3 is the coefficient of x² and in the second term, 2 is the numerical factor and it is the coefficient of x.

How Do You Identify the Factors of The Terms of an Expression?

The factors can be found in any term in the expression. It is a number or a variable multiplied to another number or a variable in the term. For example, consider the expression 3 ab. It can be written as 3 × a × b. Thus the term has 3 factors: 3, a, and b.

What are Terms of an Expression?

A term in an expression is a single number or a variable separated by a + or - sign. An expression can have one term or many terms.

Is Constant a Coefficient?

Yes, a constant is a term in the expression that has no variable. In an expression, 5n + 3, 3 is the constant and it is the coefficient of n⁰. Thus 3 is a coefficient of n⁰. All the terms in the expression have coefficients including the constant term.

What Is the numerical coefficient of 5x?

The numerical coefficient of 5x is 5. 5x denotes 5 multiplied by x.

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