factorization
An expression listing items that, when multiplied together, will produce a desired quantity.
Examples of factorization in the following topics:

Greatest Common Factor and Factoring by Grouping
 Factoring by grouping divides the terms in a polynomial into groups, which can be factored using the greatest common factor.
 Factorization or factoring is the decomposition of an object, for example, a number or a polynomial, into a product of other objects, or factors, which when multiplied together give the original.
 As an example, the number 15 factors as 3 × 5, and the polynomial $x^2 4$ factors as $(x 2)(x + 2)$.
 Factoring integers is covered by the fundamental theorem of arithmetic and factoring polynomials by the fundamental theorem of algebra.
 Factoring by grouping is done by placing the terms in the polynomial into two or more groups, where each group can be factored by a known method.

Finding Factors of Polynomials

Factoring Trinomials of the Form ax^2 + bx + c; Perfect Squares

Trinomials of the Form ax^2 + bx + c, Where a is Not Equal to 1

Finding Zeroes of Factored Polynomials
 The factored form of a polynomial reveals its zeros, which are defined as points where the function touches the x axis.
 The factored form of a polynomial can reveal where the function crosses the x axis.
 Use the factored form of a polynomial to find its zeros

Special Factorizations and Binomials

Logarithms of Products
 A useful property of logarithms states that the sum of two logarithms of factors is equal to the logarithm of the factors' product.
 Tedious multidigit multiplication steps can be replaced by table lookups and simpler addition, because of the fact that the logarithm of a product is the sum of the logarithms of the factors:
 The sum of two logarithms of factors is equal to the logarithm of the factors' product.

Adding and Subtracting with Like and Unlike Denominators

Simplifying Expressions
 If you add n more factors of a then you have n+m factors of a .
 In the same way that ${ a }^{ m }\cdot { a }^{ n }={ a }^{ m+n }$, because you are adding on factors of a, dividing is taking away factors of a.
 If you have n factors of a in the denominator, then you can cross out n factors from the numerator.
 If there were m factors in the numerator, now you have mn factors in the numerator.
 If you think about an exponent as telling you that you have so many factors of the base, then ${({a}^{n})}^{m}$ means that you have factors m of an.

Solving Quadratic Equations by Factoring