By Chance E. Gartneer
Updated Aug 30, 2022
A polynomial is a mathematical expression constructed from variables and constants using only addition, subtraction, and multiplication. Exponents applied to variables must be non‑negative integers; these exponents define the polynomial’s degree, which is crucial for solving equations and graphing.
Arrange the terms in descending order of degree. For example, the equation 2xy + 4x² + 6y³ + 1 = 0 becomes 6y³ + 4x² + 2xy + 1 = 0.
Determine the highest power of each variable present. In the example, x appears to the second power (4x²) and y to the third power (6y³).
Sum the individual highest exponents to obtain the polynomial’s overall degree. Here, 2 + 3 = 5, so the degree is 5.
For single‑variable polynomials, the degree is simply the largest exponent.
Knowing the degree tells you how many roots the polynomial can have and gives insight into the shape of its graph.
