# Degree (mathematics)

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

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 ${\displaystyle y^{5}}$.

## Related pages

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

## References

1. "Comprehensive List of Algebra Symbols". Math Vault. 2020-03-25. Retrieved 2020-08-31.
2. "Degree (of an Expression)". www.mathsisfun.com. Retrieved 2020-08-31.
3. Weisstein, Eric W. "Polynomial Degree". mathworld.wolfram.com. Retrieved 2020-08-31.