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  2. Multiplicity (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Multiplicity_(mathematics)

    This means that 1 is a root of multiplicity 2, and −4 is a simple root (of multiplicity 1). The multiplicity of a root is the number of occurrences of this root in the complete factorization of the polynomial, by means of the fundamental theorem of algebra.

  3. Polynomial expansion - Wikipedia

    en.wikipedia.org/wiki/Polynomial_expansion

    In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. Expansion of a polynomial expression can be obtained by repeatedly replacing subexpressions that multiply two other subexpressions, at least one of which is an addition, by the equivalent sum of products, continuing until the expression becomes a ...

  4. Solving quadratic equations with continued fractions - Wikipedia

    en.wikipedia.org/wiki/Solving_quadratic...

    Denoting the two roots by r 1 and r 2 we distinguish three cases. If the discriminant is zero the fraction converges to the single root of multiplicity two. If the discriminant is not zero, and |r 1 | ≠ |r 2 |, the continued fraction converges to the root of maximum modulus (i.e., to the root with the greater absolute value).

  5. Polynomial - Wikipedia

    en.wikipedia.org/wiki/Polynomial

    In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms.

  6. Bézout's theorem - Wikipedia

    en.wikipedia.org/wiki/Bézout's_theorem

    As R is a homogeneous polynomial in two indeterminates, the fundamental theorem of algebra implies that R is a product of pq linear polynomials. If one defines the multiplicity of a common zero of P and Q as the number of occurrences of the corresponding factor in the product, Bézout's theorem is thus proved.

  7. File:Polynomial roots multiplicity.svg - Wikipedia

    en.wikipedia.org/wiki/File:Polynomial_roots...

    English: Graph of the polynomial y = x^3 + 2*x^2 - 7*x + 4 with its roots (zeros) -4 and 1 marked. The root -4 is a 'simple' root (of multiplicity 1), and therefore the graph crosses the x-axis at this root. The root 1 is of even multiplicity and therefore the graph bounces off the x-axis at this root.

  8. 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]

  9. Multilinear polynomial - Wikipedia

    en.wikipedia.org/wiki/Multilinear_polynomial

    The resulting polynomial is not a linear function of the coordinates (its degree can be higher than 1), but it is a linear function of the fitted data values. The determinant, permanent and other immanants of a matrix are homogeneous multilinear polynomials in the elements of the matrix (and also multilinear forms in the rows or columns).

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