# Terms, Coefficients, Degree

Reference > Mathematics > Algebra > PolynomialsIn 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, 51x^{3}z, x^{5}, 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.

15x^{2}y: 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 14x^{3}y is 14y.

Coefficient of y in 14x^{3}y is 14x^{3}.

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.

51x^{3}z: degree = 4, because the exponents are 3 and 1.

## Questions

^{2}?

^{3}y

^{2}?

^{5}

^{4}

^{5}y

^{3}?