# 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.

*a** + 1*, *a + b*, *x ^{2 }+ 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.

#### Terms of an Expression

A term is 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 4*x + y*, the two terms are 4*x* and *y*.

It is to be noted here that terms add up to form an expression. Say there is a term 8*xy*, which is the product of 8, *x* and *y*. There is another term -4*z*, which is the product of -4 and* z*. On adding them up, 8*xy* + (-4*z*), we get 8*xy* – 4*z*, which is an algebraic expression.

#### Factor of a Term

- The numbers or variables that are multiplied to form a term are called its factors. Example, 5
*xy*is a term with factors 5,*x*and*y*. - The factors cannot be further factorized. Example, 5
*xy*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
*3a*are 3,^{4}*a, a, a*and*a*. - 1 is not taken as a separate factor.

#### Coefficient of a Term

Coefficient is the numerical factor of a term containing constant and variables.

- In the term
*5ab*, 5 is the coefficient. - -5 is the coefficient of the term –
*5ab*.^{2} - When there is no numerical factor in a term, its coefficient is taken as +1. For example, in the term
*x*, the coefficient is +1.^{2}y^{3} - In the term
*–x*, the coefficient is -1. - Coefficient is sometimes generalized as either the numerical factor, variable factor or the products of the two. As for example, in the term
*5ab*, b is the coefficient of 5^{2}*ab*. Similarly, in 10*ab*, -2*a*is the coefficient of -5*b*and so on.