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The graph of a polynomial function of degree 3. ... A composition may be expanded to a sum of terms using the rules for multiplication and division of polynomials ...
The (inverse of the) Ihara zeta function, defined as a product of binomial terms corresponding to certain closed walks in a graph. The Martin polynomial , used by Pierre Martin to study Euler tours The matching polynomials , several different polynomials defined as the generating function of the matchings of a graph.
The graph of any cubic function is similar to such a curve. The graph of a cubic function is a cubic curve, though many cubic curves are not graphs of functions. Although cubic functions depend on four parameters, their graph can have only very few shapes. In fact, the graph of a cubic function is always similar to the graph of a function of ...
In mathematics and computer science, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation.Although named after William George Horner, this method is much older, as it has been attributed to Joseph-Louis Lagrange by Horner himself, and can be traced back many hundreds of years to Chinese and Persian mathematicians. [1]
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 ...
The discriminant of a polynomial is a function of its coefficients that is zero if and only if the polynomial has a multiple root, or, if it is divisible by the square of a non-constant polynomial. In other words, the discriminant is nonzero if and only if the polynomial is square-free.
A linear function is a polynomial function in which the variable x has degree at most one: [2] = +. Such a function is called linear because its graph, the set of all points (, ()) in the Cartesian plane, is a line. The coefficient a is called the slope of the function and of the line (see below).
The graph crosses the x axis at the simple root. It is tangent to the x axis at the multiple root and does not cross it, since the multiplicity is even. The graph of a polynomial function f touches the x-axis at the real roots of the polynomial. The graph is tangent to it at the multiple roots of f and not tangent at the