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Terms, Coefficients, Degree

Reference > Mathematics > Algebra > Polynomials

In this unit we will explore polynomials, their terms, coefficients, zeroes, degree, and much more. Here we will begin with some basic terminology.

Term: A term consists of numbers and variables combined with the multiplication operation, with the variables optionally having exponents.

Examples: The following are examples of terms.

3, 3x, -2xy, 51x3z, x5, 14x-2

Numerical Coefficient: This is often abbreviated to just "coefficient." A coefficient is the numerical value in a term. If a term has no coefficient, the coefficient is an unwritten 1.

Examples: For each term below, the coefficient is stated.

3: the coefficient is 3. In this case, there are no variables, and we often refer to this as a "constant" term.
10x: the coefficient is 10.
15x2y: the coefficient is 15.

Coefficient of x: If we refer to a specific variable when talking about a coefficient, we are treating everything else besides that variable (and its exponent) as part of the coefficient.

Examples: Below are examples of terms with the stated coefficient.

Coefficient of x in 14x3y is 14y.
Coefficient of y in 14x3y is 14x3.
Coefficient of x in 12x is 12. Note that if there is only one variable, "coefficient of x" is the same as the numerical coefficient.

Degree of a term: The sum of the exponents of the term's variables. If a variable has no exponent written, the exponent is an unwritten 1.

Examples: The following are terms, with their degree stated and explained.

3: degree = 0, because there are no variables, and therefore no exponents with variables.
3x: degree = 1, because there is an unwritten exponent (1) with the x.
-2xy: degree = 2, because there are two unwritten exponents, one for each variable.
51x3z: degree = 4, because the exponents are 3 and 1.


Give three examples of terms
What is the numerical coefficient in the term 14x2?
What is the coefficient of x in the term 12x3y2?
What is the coefficient of y in the previous question?
What is the numerical coefficient in the term x5
What is the degree of the term 2x4
What is the degree of the term 3?
What is the degree of the term 2x5y3?
What is the degree of the term xy?
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