Faktorizohen

Faktorizohen is an Albanian verb meaning to factorize or to be factorized. In mathematics, factoring denotes expressing an object as a product of factors. The concept appears in number theory, algebra, and computer science, and it underpins methods for simplification, solving equations, and revealing structure.

In integers, prime factorization writes a number n > 1 uniquely as a product of primes raised to powers: n = p1^a1 p2^a2 ... pk^ak. This uniqueness, up to the order of factors, is the fundamental theorem of arithmetic. For example, 360 = 2^3 × 3^2 × 5.

In polynomials, factoring means expressing a polynomial as a product of polynomials of lower degree with coefficients in a chosen domain (integers, rationals, reals, etc.). Examples: x^2 − 5x + 6 = (x − 2)(x − 3). Techniques include factoring by inspection, factoring by grouping, and recognizing special forms such as difference of squares or perfect square trinomials. Over the rationals, Gauss's lemma and the rational root theorem guide the process; over finite fields, specialized algorithms apply.

In computation, integer factoring is regarded as a hard problem for large numbers and underlies many cryptographic systems like RSA, while polynomial factorization is routinely carried out by computer algebra systems for equation solving and simplification.

Overall, faktorizohen is a unifying operation across arithmetic and algebra, aiding simplification, problem solving, and the understanding of the structure of numbers and polynomials.