Degree (mathematics)

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

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

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

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

Related pages

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