Polynomial Degree

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A Polynomial Degree is an integer of the highest exponent in a polynomial function.

  • AKA Order of a Polynomial.
  • Context:
  • Example(s):
    • 0, for a constant and of a non-zero constant polynomial, such as [math]\displaystyle{ P(x)=3=3x^0a }[/math].
    • 1, for a variable without a written exponent, such as [math]\displaystyle{ P(x)=x=x^1 }[/math].
    • 2, for the univariate polynomial [math]\displaystyle{ P(x)=4x^2 + 10x + 1 }[/math].
    • 3, for the univariate polynomial [math]\displaystyle{ P(x)=7x^3 + 3x^2 + 4x + 1 }[/math].
    • 5, for the multivariate polynomial [math]\displaystyle{ P(x)=3xy+7x^2y^3=3x^0y^0+7x^2y^3 }[/math].
    • [math]\displaystyle{ n }[/math] for function pattern [math]\displaystyle{ P(x)=a_n x^n + a_{n-1}x^{n-1} + \dotsb + a_2 x^2 + a_1 x + a_0 }[/math], where [math]\displaystyle{ a_n }[/math] are constant terms and [math]\displaystyle{ x }[/math] is a free variable and [math]\displaystyle{ n }[/math] is the order or degree of the polynomial.
  • Counter-Example(s):
  • See: Polynomial Equation, Polynomial Function.


References