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For polynomials in two or more variables, the degree of a term is the sum of the exponents of the variables in the term; the degree (sometimes called the total degree) of the polynomial is again the maximum of the degrees of all terms in the polynomial. For example, the polynomial x 2 y 2 + 3x 3 + 4y has degree 4, the same degree as the term x ...
In mathematics, a cubic function is a function of the form () = + + +, that is, a polynomial function of degree three. In many texts, the coefficients a , b , c , and d are supposed to be real numbers , and the function is considered as a real function that maps real numbers to real numbers or as a complex function that maps complex numbers to ...
The graph of a polynomial function of degree 3. The x occurring in a polynomial is commonly called a variable or an indeterminate. When the polynomial is considered as an expression, x is a fixed symbol which does not have any value (its value is "indeterminate").
The eigenvalues of a 3×3 matrix are the roots of a cubic polynomial which is the characteristic polynomial of the matrix. The characteristic equation of a third-order constant coefficients or Cauchy–Euler (equidimensional variable coefficients) linear differential equation or difference equation is a cubic equation.
As the integrand is the polynomial of degree 3 (y(x) = 7x 3 – 8x 2 – 3x + 3), the 2-point Gaussian quadrature rule even returns an exact result. In numerical analysis , an n -point Gaussian quadrature rule , named after Carl Friedrich Gauss , [ 1 ] is a quadrature rule constructed to yield an exact result for polynomials of degree 2 n − 1 ...
For degree 3, GF(3 3) has φ(3 3 − 1) = φ(26) = 12 primitive elements. As each primitive polynomial of degree 3 has three roots, all necessarily primitive, there are 12 / 3 = 4 primitive polynomials of degree 3. One primitive polynomial is x 3 + 2x + 1. Denoting one of its roots by γ, the algebraically conjugate elements are γ 3 and γ 9.
As the degree of the Taylor polynomial rises, it approaches the correct function. This image shows sin x and its Taylor approximations by polynomials of degree 1 , 3 , 5 , 7 , 9 , 11 , and 13 at x = 0 .
Here F is a non-zero linear combination of the third-degree ... defining a quadratic extension of the field of rational functions ... Forum Geometricorum, 3: 1 ...