Polynomial Degree

The degree of a polynomial is the largest exponent appearing on its variable (with non-zero coefficient). For $3x^4 - 2x + 7$, the degree is $4$.

Names by degree:

• 0: constant ($5$)
• 1: linear ($2x + 3$)
• 2: quadratic ($x^2 + 5x + 6$)
• 3: cubic
• 4: quartic
• 5: quintic

Multivariable polynomials: degree of a term is the sum of variable exponents in that term. Degree of $4x^2 y^3$ is $5$.

The Fundamental Theorem of Algebra says a polynomial of degree $n$ has exactly $n$ roots (with multiplicity, allowing complex). Degree limits how many x-intercepts the graph can have, and how many turning points (at most $n - 1$).