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Coefficient: An expression multiplying one of the monomials of the polynomial. Root (or zero) of a polynomial: Given a polynomial p(x), the x values that satisfy p(x) = 0 are called roots (or zeroes) of the polynomial p. Graphing. End behaviour – Concavity – Orientation – Tangency point – Inflection point – Point where concavity changes.
The names for the degrees may be applied to the polynomial or to its terms. For example, the term 2x in x 2 + 2x + 1 is a linear term in a quadratic polynomial. The polynomial 0, which may be considered to have no terms at all, is called the zero polynomial. Unlike other constant polynomials, its degree is not zero.
For example, the polynomial x 2 y 2 + 3x 3 + 4y has degree 4, the same degree as the term x 2 y 2. However, a polynomial in variables x and y, is a polynomial in x with coefficients which are polynomials in y, and also a polynomial in y with coefficients which are polynomials in x. The polynomial
Polynomials: Can be generated solely by addition, multiplication, and raising to the power of a positive integer. Constant function: polynomial of degree zero, graph is a horizontal straight line; Linear function: First degree polynomial, graph is a straight line. Quadratic function: Second degree polynomial, graph is a parabola.
The numbers a, b, and c are the coefficients of the equation and may be distinguished by respectively calling them, the quadratic coefficient, the linear coefficient and the constant coefficient or free term. [2] The values of x that satisfy the equation are called solutions of the equation, and roots or zeros of the quadratic function on its ...
Leapfrog integration — another name for Verlet integration; Beeman's algorithm — a two-step method extending the Verlet method; Dynamic relaxation; Geometric integrator — a method that preserves some geometric structure of the equation Symplectic integrator — a method for the solution of Hamilton's equations that preserves the ...
Polynomial expansion; Polynomial greatest common divisor; Polynomial identity testing; Polynomial interpolation; Polynomial long division; Polynomial matrix; Polynomial matrix spectral factorization; Polynomial ring; Polynomial root-finding algorithms; Polynomial sequence; Polynomial solutions of P-recursive equations; Polynomial Wigner–Ville ...
(Note that it makes sense for such an equation to have a polynomial solution. Each term in the equation is a polynomial, and the degrees are consistent.) This is a Sturm–Liouville type of equation. Such equations generally have singularities in their solution functions f except for particular values of λ.