## The Lesson

A coefficient is a number that is placed in front of a variable. The coefficient is multiplying the variable.## Dictionary Definition

The Oxford English Dictionary defines a coefficient as "a number or quantity placed (usually) before and multiplying another quantity known or unknown."## Real Examples of Coefficients

It is easier to understand coefficients with examples.-
Consider the term below:

**6**is the coefficient of x. -
Consider the expression below. One of the coefficients is a letter rather than a number:

**a**(a constant) is the coefficient of x^{2}.**1**is the coefficient of x, even though no number or letter is written in front of it (see**Note**).**2**is the coefficient of y.

## Understanding Coefficients

Think of a letter in algebra as an object. We can count the objects.**x**is one

**x**. If we add one

**x**to one

**x**, we get two

**x**'s.

**x**+

**x**=

**2x**

**x**'s. Another way of saying this is that the 2 is multiplying the

**x**after it:

**2x**=

**2**×

**x**=

**x**+

**x**

**x**, we would have 3

**x**'s:

**3x**=

**3**×

**x**=

**x**+

**x**+

**x**

## Letters As Coefficients

Letters can be used as coefficients. For example, a standard linear equation is*y = mx + c*. The

**m**is the coefficient of the x term.The letter still represents a number. The

**m**could be a 2 or a −3 for different linear equations.

## A Term Without a Number in Front of it Has a Coefficient of 1

Sometimes a term will not have a number in front of it.Don't be fooled. It still has a coefficient. The coefficient is

**1**.