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
 Hench, one can "factor out," or "pull out," 2x.
 The second type of factoring is based on the "squaring" formulae:
 x2+4 is a perfectly good function, but it cannot be factored.
 Show how to factor a polynomial by reversing the FOIL process
 Practice factoring a polynomial by pulling out the greatest common factor

Trinomials of the Form ax^2 + bx + c, Where a is Not Equal to 1
 Two methods for factoring polynomials $ax^2 + bx + c$ are the trial and error method and the collect and discard method.
 We can easily factor trinomials of the form $ax^2 + bx + c$ by finding the factors of the constant c that add to the coefficient of the linear term b, as shown in the following example:
 The problem of factoring the polynomial $ax^2+bx+c$, $a \neq 1$, becomes more involved.
 Examining a trinomial, we look for some factors of the first and last terms.
 Find the factors of 72 that add to 1, the coefficient of x, the linear term.

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

Factoring Trinomials of the Form ax^2 + bx + c; Perfect Squares
 The polynomial $ax^2 + bx + c$ can be factored using a variety of methods, including trial and error.
 Ultimately, the trinomial should be factored in the form $(px+q)(rx+s)$, where p, q, r, and s are constants, and x is a variable.
 Some trinomials, known as perfect square trinomials, can be factored into two equal binomials.
 Perfect square trinomials always factor as the square of a binomial.
 Apply factoring techniques to factor a trinomial of the form ax2 + bx + c

Special Factorizations and Binomials
 Since we know that $(a + b)(a b) = a^2 b^2$, we need only turn the equation around to find the factorization form:
 The factorization form says that we can factor $a^2 b^2$, the difference of two squares, by finding the terms that produce the perfect squares and substituting these quantities into the factorization form.
 When using real numbers (as we are), there is no factored form for the sum of two squares.
 That is, using real numbers, a2 + b2 cannot be factored.
 Perfect square trinomials always factor as the square of a binomial.

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
 Because 12=2×2×3, any number whose prime factors include two 2s and one 3 will be a multiple of 12.
 Similarly, any number whose prime factors include a 2, a 3, and a 5 will be a multiple of 30.
 It is best to leave the bottom alone, since it is factored.
 But finally, we note that we can factor the top again.
 If we factor out an x it will cancel with the x in the denominator.

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
 Quadratic equations can be solved by factoring, completing the square, graphing, Newton's method, and using the quadratic formula.
 To solve quadratic equations by factoring, lets remember the FOIL property.
 Before we jump into factoring out a quadratic equation, lets try to FOIL a function:
 Remembering this, lets think about how we need to go about factoring out a quadratic equation.