faktorizimin

Faktorizimi, or faktorizimin in Albanian, is the process of expressing a mathematical object as a product of factors. In mathematics, it is used for integers and polynomials, among other structures, to reveal simpler components.

Integer faktorizimi decomposes a positive integer into prime factors. The fundamental theorem of arithmetic states that every integer greater than 1 has a unique prime factorization up to the order of the factors. For example, 60 = 2^2 × 3 × 5. Prime factorization facilitates simplification, solving equations, and number-theoretic analysis. Finding factors for large numbers is computationally difficult, which underpins the security of many cryptographic systems.

Polynomial faktorizimi involves decomposing a polynomial into a product of polynomials of smaller degree, ideally irreducible polynomials over a chosen field. Over the rationals, for example, x^2 − 5x + 6 factors as (x − 2)(x − 3). General factoring uses methods such as inspection, the rational root theorem, and, for higher degrees, algorithmic approaches when factoring over finite fields or extensions.

The concept of faktorizimi is foundational in algebra and number theory. It helps simplify expressions, solve equations, and understand the internal structure of mathematical objects. In Albanian usage, the definite form faktorizimin appears in contexts like “procesi i faktorizimit” (the process of factorization).