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elementary algebra
In ________, factoring a polynomial reduces the problem of finding its roots to finding the roots of the factors.
Matrices
________ possess many kinds of matrix factorizations.
efficient computer algorithms
There are ________ for computing (complete) factorizations within the ring of polynomials with rational number coefficients (see factorization of polynomials)
mathematical object
Factorization may also refer to more general decompositions of a(n) ________ into the product of smaller or simpler objects.
commutative ring
A(n) ________ possessing the unique factorization property is called a unique factorization domain.
Factorization
________ was first considered by ancient Greek mathematicians in the case of integers.
In particular, a univariate polynomial with complex coefficients admits a unique (up to ordering) factorization into linear polynomials
this is a version of the fundamental theorem of algebra
However, rings of algebraic integers satisfy the weaker property of Dedekind domains
ideals factor uniquely into prime ideals
