Definition - Degree of the Polynomial or Function

Degree - The greatest exponent in a polynomial or equation.

Example:

•  3x¹³ + 5x³ (Degree: 13)
  
  
• h⁵ + h⁴ + h⁸ + h³ + h¹² + h² +  13h (Degree: 12)
  
  
• y = -5b + 19 (Degree : 1; Note, b is raised to the 1^st power.)
  
  
• ƒ(x) = 5x⁹ - 5 (Degree: 9)

Why is This Important?

• The degree of a function determines the most number of solutions that the function could have.
• The degree of a function determines the most number of times a function will cross the x-axis.

Examples

• y = x (Degree: 1; Only 1 solution)
• y = x² (Degree: 2; Two possible solutions)
• y = x³ (Degree: 3; Three possible solutions)