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  2. Degree of a polynomial - Wikipedia

    en.wikipedia.org/wiki/Degree_of_a_polynomial

    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 ...

  3. Cubic function - Wikipedia

    en.wikipedia.org/wiki/Cubic_function

    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 ...

  4. Polynomial long division - Wikipedia

    en.wikipedia.org/wiki/Polynomial_long_division

    Polynomial long division is an algorithm that implements the Euclidean division of polynomials, which starting from two polynomials A (the dividend) and B (the divisor) produces, if B is not zero, a quotient Q and a remainder R such that A = BQ + R, and either R = 0 or the degree of R is lower than the degree of B.

  5. Polynomial - Wikipedia

    en.wikipedia.org/wiki/Polynomial

    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").

  6. Descartes' rule of signs - Wikipedia

    en.wikipedia.org/wiki/Descartes'_rule_of_signs

    [2] [3] In the 1970s Askold Khovanskii developed the theory of fewnomials that generalises Descartes' rule. [4] The rule of signs can be thought of as stating that the number of real roots of a polynomial is dependent on the polynomial's complexity, and that this complexity is proportional to the number of monomials it has, not its degree.

  7. Horner's method - Wikipedia

    en.wikipedia.org/wiki/Horner's_method

    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]

  8. Synthetic division - Wikipedia

    en.wikipedia.org/wiki/Synthetic_division

    E.g.: x**2 + 3*x + 5 will be represented as [1, 3, 5] """ out = list (dividend) # Copy the dividend normalizer = divisor [0] for i in range (len (dividend)-len (divisor) + 1): # For general polynomial division (when polynomials are non-monic), # we need to normalize by dividing the coefficient with the divisor's first coefficient out [i ...

  9. Division polynomials - Wikipedia

    en.wikipedia.org/wiki/Division_polynomials

    In mathematics the division polynomials provide a way to calculate multiples of points on elliptic curves and to study the fields generated by torsion points. They play a central role in the study of counting points on elliptic curves in Schoof's algorithm .