Terms, Coefficients, DegreeReference > 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.