What Is A Coefficient ?

In mathematics, a coefficient is an integer that is multiplied with the variable of a single term or the terms of a polynomial. It is usually a number, but sometimes may be replaced by a letter in an expression. For example, in the expression: ax2 + bx + c, x is the variable and 'a' and 'b' are the coefficients.

What Is a Coefficient?
A coefficient refers to a number or quantity placed with a variable. It is usually an integer that is multiplied by the variable next to it. The variables which do not have a number with them are assumed to be having 1 as their coefficient. For example, in the expression 3x, 3 is the coefficient but in the expression x2 + 3, 1 is the coefficient of x2. In other words, a coefficient is a multiplicative factor in the terms of a polynomial, a series, or any expression. It is generally a number. Observe the following expression which shows that 5 is the coefficient of x2 and 8 is the coefficient of y.

Coefficient Example

How To Find a Coefficient?
In order to find a coefficient, the most important thing that should be remembered is that it always comes with a variable. Let us understand this with the help of the example: 5x2+2y-7. In this expression, we can see that there are three terms: 5x2, 2y, 7. In the first term 5x2, x is the variable and as we know that a coefficient always comes with the variable, the coefficient is 5. In the second term 2y, y is the variable, so the coefficient is 2. In the third term, 7 is known as the constant.

Numerical Coefficient
A numerical coefficient is a number that is the multiplier of the variables in a term. For example, 3 is the numerical coefficient of the term 3mn. The term numerical coefficient is used for the constant multipliers of the variable. A common example is 4xy. Here, the numerical coefficient of xy is 4.

Characteristics of a Coefficient
A coefficient can be positive or negative, real or imaginary, or in the form of decimals or fractions. Another definition of coefficient says, “Any number with which we multiply a variable." For example, in the term 9.3x, 9.3 is the coefficient of the variable x, and in -5z, -5 is the coefficient.

Important Notes

Keep the following points in mind while working with coefficients:

A coefficient is always attached to a variable.
A variable without a number has 1 as its coefficient.
The value of a variable is never the same. It varies according to the question and situation, and therefore, it is called a variable.
The value of a constant is constant because its value is always fixed, and it cannot be changed.