Terms, Factors and Coefficients of Expression

Terms, Factors and Coefficients of Expression:

1. Terms:

• Terms are added to form expressions. Terms are added to make an expression.

• For example, the terms 4x² and (- 3xy) are added to give the expression 4x² – 3xy. This is because 4x² + (- 3xy) = 4x² – 3xy.

• Note, the minus sign (–) is included in the term.

2. Factors:

A term is a product of factors. The term 4xy in the expression 4xy + 7 is a product of factors x, y, and 4. Factors containing variables are said to be algebraic factors.

The expression (4x² – 3xy) consists of two terms 4x² and – 3xy. The term 4x² is a product of 4, x, and x; we say that 4, x, and x are the factors of the term 4x². A term is a product of its factors. The term – 3xy is a product of the factors –3, x, and y.

3. Coefficient:

• The coefficient is the numerical factor in the term. Sometimes any one factor in a term is called the coefficient of the remaining part of the term.

• In the term 10xyz, 10 is the coefficient of xyz, in the term -7x²y², - 7 is the coefficient of x²y².

• When the coefficient of a term is + 1, it is usually omitted. For example, 1x is written as x; 1x²y² is written as x²y², and so on. Also, the coefficient (– 1) is indicated only by the minus sign.
  Thus (– 1) x is written as – x; (–1) x² y ² is written as – x² y² and so on.
• Sometimes, the word 'coefficient' is used in a more general way. Thus we say that in the term 5xy, 5 is the coefficient of xy, x is the coefficient of 5y and y is the coefficient of 5x. In 10xy², 10 is the coefficient of xy², x is the coefficient of 10y² and y² is the coefficient of 10x.
  Thus, in this more general way, a coefficient may be either a numerical factor or an algebraic factor or a product of two or more factors. It is said to be the coefficient of the product of the remaining factors.