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Degree of a Term

Degree of a Term

For a term with one variable, the degree is the variable's exponent. With more than one variable, the degree is the sum of the exponents of the variables.

 

Table showing terms and degrees: -5x⁷ (degree 7), 3x (degree 1), 9x²y⁴ (degree 6), ab (degree 2), 12 (degree 0).

Key Formula

degree of   a x1n1 x2n2⋯xknk=n1+n2+⋯+nk\text{degree of } \; a\,x_1^{n_1}\,x_2^{n_2}\cdots x_k^{n_k} = n_1 + n_2 + \cdots + n_k
Where:
  • aa = The numerical coefficient (any nonzero constant)
  • x1,x2,…,xkx_1, x_2, \ldots, x_k = The variables in the term
  • n1,n2,…,nkn_1, n_2, \ldots, n_k = The exponents on each variable (must be nonneg. integers)

Worked Example

Problem: Find the degree of the term 7x^3y^2z.
Step 1: Identify each variable and its exponent. Here x has exponent 3, y has exponent 2, and z has exponent 1 (since z means z^1).
x3,  y2,  z1x^3,\; y^2,\; z^1
Step 2: Add all the exponents together.
3+2+1=63 + 2 + 1 = 6
Step 3: The coefficient 7 does not affect the degree. It only multiplies the term.
Answer: The degree of 7x³y²z is 6.

Another Example

Problem: Find the degree of each term: (a) 5x^4, (b) −9, (c) 2ab^3.
(a): The only variable is x with exponent 4, so the degree is 4.
degree=4\text{degree} = 4
(b): The term −9 is a constant with no variable. A nonzero constant is considered to have degree 0.
degree=0\text{degree} = 0
(c): Variable a has exponent 1 and variable b has exponent 3. Add them.
1+3=41 + 3 = 4
Answer: (a) degree 4, (b) degree 0, (c) degree 4.

Frequently Asked Questions

What is the degree of a constant term like 5 or −3?
A nonzero constant has degree 0. You can think of 5 as 5x^0, because x^0 = 1. The special case is the constant 0, which is usually said to have no degree (or an undefined degree).
How is the degree of a term different from the degree of a polynomial?
The degree of a term looks at one single term. The degree of a polynomial is the highest degree among all of its terms. For example, in 3x^4 + 2x^2 − x, the individual term degrees are 4, 2, and 1, so the polynomial's degree is 4.

Degree of a term vs. Degree of a polynomial

The degree of a term is the sum of exponents in that single term. The degree of a polynomial is the largest degree found among all its terms. For instance, in 6x^3y + 2x^2 − 1, the term 6x^3y has degree 4, 2x^2 has degree 2, and −1 has degree 0, so the polynomial's degree is 4.

Why It Matters

Knowing the degree of each term lets you classify polynomials (linear, quadratic, cubic, etc.) and arrange them in standard form. It also determines how a function behaves for very large or very small inputs—higher-degree terms dominate the graph's shape. In algebra and calculus, identifying degree is one of the first steps when simplifying, factoring, or dividing expressions.

Common Mistakes

Mistake: Forgetting that a variable written without an exponent (like y) actually has an exponent of 1.
Correction: Always treat a bare variable as having exponent 1. So in the term 4xy^2, the degree is 1 + 2 = 3, not just 2.
Mistake: Including the coefficient's value when calculating the degree.
Correction: The coefficient (the number in front) has no effect on the degree. In 8x^3 the degree is 3, not 3 + 8 or anything involving 8.

Related Terms

  • Variable — The letter whose exponent determines degree
  • Exponent — The power that defines a term's degree
  • Sum — Exponents are summed for multivariable terms
  • Polynomial — Expression whose degree depends on its terms
  • Coefficient — Numeric factor that does not affect degree
  • Monomial — A single-term polynomial with a degree
  • Leading Term — Term with the highest degree in a polynomial