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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...


Consider 18wz - 24w + 15z - 20

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

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 pair-wise, 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
  1. There are four terms
  2. Fewer than three terms are perfect squares (if three terms are perfect squares, look for the combination of a perfect square trinomial and the difference of two squares, described on the factoring page.)
  3. Pairs of terms have factors in common.

 Related pages in this website

Next: Trinomials.


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