Factorization means to decompose a number or polynomial into a product of other objects, called factors, which when multiplied together gives the original number or polynomial.
Ex. The number 16 = 2*2*2*2 when factorized into prime numbers. Since prime-numbers can’t be factorized it is the final stage of factorization of numbers.
Also polynomials can be factorized with e.g. the conjugate rule
x4 -1 = (x2-1)(x2+1) = (x-1)(x+1)(x2+1)
or with the theorem of factorization stating that the roots of a polynomial are also factors of that polynomial.
Consider the polynomial p(x) = (x-2)(x-3).
As can easily be seen the roots of p(x) are x = 2 and x = 3.
Multiplying the parentheses results in
p(x) = x2 – 5x + 6.
x2 – 5x + 6 = (x-2)(x-3)
Therefore the roots to this polynomial are also the factors of it!