# What is a Coefficient?

Definition: A coefficient, commonly found in financial formulas, is the number that a factor is multiplied by. In other words, it represents the number of times a number is added to itself.

## What Does Coefficient Mean?

What is the definition of coefficient? The coefficient is an important concept in mathematics, and provides the foundation for multiplication, division, and many other forms of mathematics. Coefficients are used by many professions, indeed by anybody that uses multiplication, and is thus involved in several areas: physics, all types of engineering, finance, and many other professions. Since the coefficient is vital to math, and math is an important underpinning to many careers, the coefficient is used all over the spectrum.

Let’s look at an example.

## Example

Mark is the head of engineering at an aerospace company that creates and manufactures airliner engines. In order to educate new interns and employees, he holds a weekly meetings that review mathematics and engineering concepts that are vital to a position with the firm.

Mark stresses a large variety of concepts, both basic and advanced, but one thing he continually stresses is the importance of knowing what the coefficient in your equation is and to double check if it is correct. In order to better relate to the attendees, he provides a few examples, and starts with a simple equation. He starts with the quadratic equation of ax^2 + bx + c, and points out the coefficients in the equation. First, he points out that “a” is the coefficient of x^2, and that b is the coefficient of x.

He next explains the importance that these coefficients play: in an aerospace engineering role, you will have many different coefficients, and the equation would look drastically different if you choose 5 instead of 4 for the coefficients a and b: 5x^2 + 5x + c versus 4x^2 + 4x + c. Now, let’s say that x = 2 and c = 5. The results would look like this, respectively: 5(2^2) + 5(2) + 5 = 35, and 4(2^2) + 4(2) + 5 = 29. The coefficient is a very powerful tool in mathematics, and Mark’s lessons tend to impress this upon the new employees.

## Summary Definition

Define Coefficients: Coefficient means an expression in a mathematically to be multiplied.

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