Definition, Examples | Coefficient Of A Variable - Cuemath

Coefficient

In mathematics, a coefficient is a number or any symbol representing a constant value that is multiplied by 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.

1.	What is a Coefficient?
2.	Coefficient of a Variable
3.	How to Find a Coefficient?
4.	Numerical Coefficient
5.	Leading Coefficient
6.	FAQs on Coefficient

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 and written 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 of x 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. Observe the following expression which shows that 5 is the coefficient of x2 and 8 is the coefficient of y.

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.

Coefficient of a Variable

The coefficient of a variable is the value of the integer or any letter that is present with the variable. For example, the coefficient of variable x in the expression 2x + 3y is 2, and in the same expression, the coefficient of variable y is 3. Similarly, the coefficient of the variable x2 in the quadratic expression ax2 + bx + c is a.

How to Find a Coefficient?

To find a coefficient of a variable in a term, follow the steps given below:

• Step 1: Encircle the variable along with its power whose coefficient we are finding.
• Step 2: Leave that variable and consider all other numbers or variables written with it. That will be the coefficient.

For example, let us find the coefficients of x and y in the term 5xy. To find the coefficient of x, we can encircle it or underline it. Then, take everything else except for x, i.e. 5y. So, the coefficient of x in the term 5xy is 5y. Similarly, the coefficient of y in the term 5xy is 5x.

In order to find acoefficient, 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, and -7. In the first term 5x2, x2 is the variable and as we know that a coefficient always comes with the variable, so 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, not a coefficient.

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.

Leading Coefficient

When a polynomial is written in its standard form, then the coefficient of the term containing the degree or the coefficient written with the first term is called the leading coefficient. In other words, it is the coefficient of the term with the highest power in an expression. Look at the image below showing the leading coefficient in the general form of a polynomial.

Some of the examples of the leading coefficient in polynomials are given below:

• In the expression 4a2 - 7a + 9, the leading coefficient is 4.
• In 3xy - 9x + 4, the leading coefficient is 3.
• In 17 - 3x3 + 5xy + 8x, the leading coefficient is -3.

Tips and Tricks on Coefficient

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.
• We cannot have 0 as the coefficient, as the value of the term with 0 as the coefficient is 0.

Thinking Out Of the Box!

• Can a variable be a coefficient?
• Can a fraction be a coefficient?

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