Degree (mathematics)

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

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

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

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

Related pages

• Fundamental theorem of algebra, a theorem which states that a polynomial of degree <math>n</math> has <math>n</math> complex roots.