Degree (mathematics)

For the corresponding concept in geometry, see Degree (angle).

The degree of a polynomial $p(x)$ is the highest exponent that occurs inside that polynomial. It is represented by the symbol $\deg(p(x))$.

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

The name of the variable is not important. For example, the polynomial $-6y^{5}+2y^{3}-25y-58$ has degree $5$, because the highest power of the variable, in this case $y$, is $5$, which occurs in the term $y^{5}$.

Related pages

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