
This is the second page about factoring. It helps you find PAIRS OF FACTORS.
In the first page, I presented the perfect square trinomial and the difference of two squares.
Here, I will present a method of factoring polynomials with four terms in which pairs of terms have factors in common.
I'll start with an example...
EXAMPLE 5:

Step 1: Notice that pairs of terms have factors in common: 18wz and 24w have 6w in common. 18wz and 15z have 3z in common.
Step 2: Arrange the terms at the corners of a square, so that terms sharing factors share a side, and terms sharing few factors are diagonally opposite one another, like this:
18wz  24w  


15z  20 
Step 3: Start on any side by writing the largest factor shared by the corners, like this:
18wz  6w  24w  


15z  20 
Step 4: Now continue around the square this way: divide the corner by the edge to get the other edge attached to this corner. Pay attention to the plus and minus signs, like this:
18wz  6w  24w  
3z 

4  
15z  5  20 
Step 5: Finally, collect terms on opposite edges. In this example, collect 3z and 4, and collect 6w and 5. The final factoring looks like this:
(3z  4) (6w + 5)
Check your answer using F.O.I.L. (Multiply pairwise, the first terms, then the outer terms, inner terms, and last terms, and add up the products.) When you do, you'll get this:
18wz +15z 24w  20
How to recognize PAIRS OF FACTORS 

Next: Trinomials.
The webmaster and author of this Math Help site is Graeme McRae.