Faktorizáció

Faktorizáció is a mathematical term referring to the process of breaking down a number or algebraic expression into its factors. Factors are numbers or expressions that divide evenly into the original number or expression. For instance, the factors of the number 12 are 1, 2, 3, 4, 6, and 12. When we talk about factorization in the context of integers, we often mean prime factorization, where a number is expressed as a product of its prime factors. For example, the prime factorization of 12 is 2 x 2 x 3, or 2^2 x 3.

In algebra, factorization involves rewriting a polynomial as a product of simpler polynomials. This is a fundamental technique used to solve equations, simplify expressions, and understand the roots of polynomials. Common factorization methods include finding a common factor, difference of squares, sum or difference of cubes, and factoring by grouping. For example, the expression x^2 - 4 can be factored into (x - 2)(x + 2) using the difference of squares formula. Factoring is crucial in various areas of mathematics, including number theory, algebra, and calculus, enabling deeper analysis and problem-solving.