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Definition - Degree of the Polynomial or Function

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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 1st 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)
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