Identify the GCF in the expression. For example, in the expression 12x^3 - 6x^2 + 2x, the greatest common factor is 2x, because it is the largest term that can be divided out of each term in the expression.
Divide out the GCF from each term. This leaves 6x^2 - 2x + 1.
Place the GCF at the front of the expression as a separate factor. This results in (2x)(6x^2 - 2x + 1).
Group the first two terms together and the last two terms together, leaving the sign between them intact. For example, the expression x^3 + 3x^2 + 2x + 6 becomes (x^3 + 3x^2) + (2x + 6).
Identify the GCF in each of the two binomials. In the above example, the GCF of (x^3 + 3x^2) is x^2. The GCF of (2x + 6) is 2. This yields x^2(x + 3) + 2(x + 3).
Factor out the common binomial and place it in front. In the example, (x + 3) is the common binomial. This results in (x + 3)(x^2 + 2).
Place two sets of parentheses next to each other to hold the two terms that you will end up with. When you multiply these two terms together, it should result in the original expression.
Find the factors for the first position in each term. For example, in the expression x^2 + 8x + 15, the first term is x^2. To get this, you need an "x" in the first position of each term. This results in (x )(x ).
Determine the factors for the last position. For this, you need two numbers whose product is 15 and whose sum is 8. These numbers are 5 and 3, because 5 x 3 = 15, and 5 + 3 = 8. Placing these in the terms yields (x + 5)(x + 3). When this is multiplied back out, it results in the original expression.