Coefficients: Definition & Concept

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  • 0:00 Coefficients Defined
  • 1:24 Leading Coefficients
  • 2:46 Lesson Summary
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Lesson Transcript
Instructor: DaQuita Hester

DaQuita has taught high school mathematics for six years and has a master's degree in secondary mathematics education.

Coefficients come in different forms and can tell you many things about a graph. Learn more about coefficient in this lesson, and check your understanding with a quiz.

Coefficients Defined

Coefficients are the multiplicative numbers located directly in front of a variable, such as x or y. If a number in an equation is not connected with a variable, that number is not considered a coefficient. Instead, it is called a constant. Coefficients can be positive or negative and real or imaginary, as well as decimals, fractions, or whole numbers. Let's take a look at some examples:

  • In the term 5x, the coefficient is the number 5. This coefficient is a whole number that is positive and real.
  • In the term -3y, the coefficient is the number -3. This coefficient is a whole number that is negative and real.
  • For an imaginary coefficient, let's examine the term 2ix. The coefficient for this term is 2i, which is an imaginary whole number.
  • Now, let's look at 3.5z. For this term, 3.5 is our decimal coefficient.

It is important to note that all variables will have a coefficient. If a variable is written without a coefficient, then it is assumed to have a coefficient of 1; frequently, when the coefficient is 1, it is not written. An example of this would be in the equation x + 6. There is no coefficient presented with the variable, so the term x has a coefficient of 1.

Leading Coefficients

A leading coefficient is the coefficient of a term with the highest degree, or largest exponent, within an equation. For example, the degree of the equation 6y^4 + 5y^2 - 2y + 1 is 4, because that is the largest exponent. Therefore, the leading coefficient is 6.

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