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Unit 2 - Factorization

Intro
Factorization (or factoring) is the breaking down of a mathematical object (i.e. number, monomial, or polynomial) into a product of other objects. These other objects are called factors. When factors are multiplied together, they create the original object that are factored.

For example, the number 6 factors into primes as 2 × 3, and the polynomial  factors as . In all cases of factoring, a product of simpler objects is obtained.

The aim of factoring is generally to reduce something to “basic building blocks”. This means numbers would be factored to prime numbers and polynomials would be factored to irreducible polynomials. 

Expansion is the the opposite of polynomial factorization. This was covered in previous math courses and in our earlier units. Understanding of how expansion works in paramount in understanding how factoring works.

Integer factorization for large integers appears to be a difficult problem. There is no known method to carry it out quickly. Its complexity is the basis of the assumed security of some public key cryptography algorithms, such as RSA.