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2. Factorization - Wikipedia

   en.wikipedia.org/wiki/Factorization

   In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5 is an integer factorization of 15, and (x – 2)(x + 2) is a polynomial ...

3. Factorization of polynomials - Wikipedia

   en.wikipedia.org/wiki/Factorization_of_polynomials

   If the original polynomial is the product of factors at least two of which are of degree 2 or higher, this technique only provides a partial factorization; otherwise the factorization is complete. In particular, if there is exactly one non-linear factor, it will be the polynomial left after all linear factors have been factorized out.

4. Factorization of polynomials over finite fields - Wikipedia

   en.wikipedia.org/wiki/Factorization_of...

   In practice, algorithms have been designed only for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them. All factorization algorithms, including the case of multivariate polynomials over the rational numbers, reduce the problem to this case; see polynomial ...

5. Factor theorem - Wikipedia

   en.wikipedia.org/wiki/Factor_theorem

   In algebra, the factor theorem connects polynomial factors with polynomial roots. Specifically, if f ( x ) {\displaystyle f(x)} is a polynomial, then x − a {\displaystyle x-a} is a factor of f ( x ) {\displaystyle f(x)} if and only if f ( a ) = 0 {\displaystyle f(a)=0} (that is, a {\displaystyle a} is a root of the polynomial).

6. Matrix factorization of a polynomial - Wikipedia

   en.wikipedia.org/wiki/Matrix_factorization_of_a...

   In mathematics, a matrix factorization of a polynomial is a technique for factoring irreducible polynomials with matrices. David Eisenbud proved that every multivariate real-valued polynomial p without linear terms can be written as AB = pI , where A and B are square matrices and I is the identity matrix . [ 1 ]

7. Pollard's rho algorithm - Wikipedia

   en.wikipedia.org/wiki/Pollard's_rho_algorithm

   The algorithm is used to factorize a number =, where is a non-trivial factor. A polynomial modulo , called () (e.g., () = (+)), is used to generate a pseudorandom sequence.It is important to note that () must be a polynomial.

8. Man documents inflated grocery prices in Alaskan hometown ...

   www.aol.com/man-documents-inflated-grocery...

   The price of milk was $12.69 per gallon, a carton of 18 eggs was $10.79, a 5-pound bag of flour was on sale for $12.99, a regular bag of nacho cheese-flavored chips was $11.29, a 12-pack of soda ...

9. Hensel's lemma - Wikipedia

   en.wikipedia.org/wiki/Hensel's_lemma

   Hensel's original lemma concerns the relation between polynomial factorization over the integers and over the integers modulo a prime number p and its powers. It can be straightforwardly extended to the case where the integers are replaced by any commutative ring, and p is replaced by any maximal ideal (indeed, the maximal ideals of have the form , where p is a prime number).