Factorizes

Factorizes is a term used in mathematics to describe the process of breaking down a number or an algebraic expression into its factors. Factors are numbers or expressions that divide another number or expression evenly, without leaving a remainder. For instance, the factors of the number 12 are 1, 2, 3, 4, 6, and 12. When we say 12 factorizes into 3 and 4, it means that 3 multiplied by 4 equals 12.

In number theory, prime factorization is a fundamental concept. It involves expressing a composite number as a product of its prime factors. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. For example, the prime factorization of 12 is 2 x 2 x 3. Every integer greater than 1 can be uniquely factorized into a product of prime numbers, according to the fundamental theorem of arithmetic.

In algebra, factorizing expressions involves rewriting them as a product of simpler expressions, often called factors. This can be useful for solving equations, simplifying expressions, or understanding the structure of a polynomial. For example, the quadratic expression x² - 4 can be factorized into (x - 2)(x + 2). Various techniques exist for algebraic factorization, including factoring out common factors, using identities like the difference of squares or perfect square trinomials, and factoring by grouping. The process of factorizing is essentially the reverse of multiplication.