Degree (mathematics)

For the similarly named unit in geometry, see Degree (angle).

The degree of a polynomial ${\displaystyle p(x)}$ is the highest exponent that occurs inside that polynomial.^[1][2][3] It is represented by the symbol ${\displaystyle \deg(p(x))}$.

For example, if we look at the polynomial ${\displaystyle 2x^{3}-7x^{2}+5x-4}$, then we can see that the degree of this polynomial is ${\displaystyle 3}$, because the highest power in the variable ${\displaystyle x}$ is ${\displaystyle 3}$. It occurs in the term ${\displaystyle x^{3}}$.

The name of the variable is not important. For example, the polynomial ${\displaystyle -6y^{5}+2y^{3}-25y-58}$ has degree ${\displaystyle 5}$, because the highest power of the variable, in this case ${\displaystyle y}$, is ${\displaystyle 5}$, which occurs in the term ${\displaystyle y^{5}}$. Polynomials with more than one variable add up the power of each variable in a term to determine the degree: for example, ${\displaystyle x^{4}y^{2}}$ is a term of degree 6.

Related pages

• Fundamental theorem of algebra, a theorem which states that a polynomial of degree ${\displaystyle n}$ has ${\displaystyle n}$ complex roots.