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The polynomial x 2 + cx + d, where a + b = c and ab = d, can be factorized into (x + a)(x + b).. 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.
This restricted applicability has made Euler's factorization method disfavoured for computer factoring algorithms, since any user attempting to factor a random integer is unlikely to know whether Euler's method can actually be applied to the integer in question. It is only relatively recently that there have been attempts to develop Euler's ...
The worksheets support Markdown and HTML for decoration, and R, Octave, Cython, Julia and others for programming in addition to Sage. CoCalc supports Jupyter notebooks , which are enhanced with real-time synchronization for collaboration and a history recording function.
If two or more factors of a polynomial are identical, then the polynomial is a multiple of the square of this factor. The multiple factor is also a factor of the polynomial's derivative (with respect to any of the variables, if several). For univariate polynomials, multiple factors are equivalent to multiple roots (over a suitable extension field).
Factoring (finance), a form of commercial finance; Factorization, the mathematical concept of splitting an object into multiple parts multiplied together; Integer factorization, splitting a whole number into the product of smaller whole numbers; Decomposition (computer science) A rule in resolution theorem proving, see Resolution (logic)#Factoring
The problem that we are trying to solve is: given an odd composite number, find its integer factors. To achieve this, Shor's algorithm consists of two parts: A classical reduction of the factoring problem to the problem of order-finding.