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):
- a Taylor Series, because it has an infinite number of function terms.
- See: Polynomial Equation, Polynomial Function.