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In [[mathematics]], '''factorization''' or '''factoring''' is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a [[multiplication|product]] of other objects, or '''factors''', which when [[multiplication|multiplied]] together give the original. For example, the number 15 factors into [[prime number|primes]] as 3 × 5; and the [[polynomial]] ''x''<sup>2</sup> − 4 factors as (''x'' − 2)(''x'' + 2). In all cases, we obtain a product of simpler things.
The aim of factoring is usually to reduce something to "basic building blocks", such as numbers to prime numbers, or polynomials to [[irreducible polynomial|irreducible polynomials]]. Factoring integers is covered by the [[fundamental theorem of arithmetic]] and [[polynomial factorization|factoring polynomials]] by the [[fundamental theorem of algebra]].
The opposite of factorization is [[polynomial expansion|expansion]]. This is the process of multiplying together [[divisor|factors]] to recreate the original, "expanded" [[polynomial]].
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