Factoring in Algebra I
Factoring algebraic expressions is one of the most important techniques you need to practice. Not much else can be done in terms of solving equations, graphing functions and conics, and working on math applications if you can’t pull out a common factor and simplify an expression. Factoring is crucial, essential, and basic to algebra.

Make sure you apply divisibility rules correctly.

Write a prime factorization with the correct exponents on the prime factors.

Check that the terms divided after dividing out a greatest common factor (GCF) don’t still have a common factor.

Reduce only factors, not terms.

Write fractional answers with correct grouping symbols to distinguish remaining factors.
Factoring Binomials
A binomial is an expression with two terms. The terms can be separated by addition or subtraction. You have four possibilities for factoring binomials:

Factor out a greatest common factor.

Factor as the difference of perfect squares.

Factor as the difference of perfect cubes.

Factor as the sum of perfect cubes.
If one of these methods doesn’t work, then the binomial doesn’t factor by using real numbers.
Factoring Quadratic Trinomials
You can factor trinomials with the form ax^{2} + bx + c in one of two ways:

Factor out a greatest common factor.

Find two binomials whose product is that trinomial.
When finding the two binomials whose product is a particular trinomial, you work from the factors of the constant term and the factors of the coefficient of the lead term to create a sum or difference that matches the coefficient of the middle term. This technique can be expanded to trinomials that have the same general format but with exponents that are multiples of the basic trinomial.