# 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, 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.

#### 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 4x + y, the two terms are 4x and y.

It is to be noted here that terms add up to form an 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.

#### Factor of a Term

• The numbers or variables that are multiplied to form a term are called its factors. Example, 5xy is a term with factors 5, x and y.
• The factors cannot be further factorized. 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.

#### 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 –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.
• Coefficient is sometimes generalized as either the numerical factor, variable factor or the products of the two. As for example, in the term 5ab2, b is the coefficient of 5ab. Similarly, in 10ab, -2a is the coefficient of -5b and so on.