It may be possible to factor a polynomial containing four or more terms by factoring common monomials from groups of terms. This method is called factoring by grouping. The following example illustrates how this process works.
Our polynomial is now factored completely.
- We find the product ac.
- We look for two numbers that multiply to give ac and add to give b.
- We rewrite the middle term using the two numbers we just found.
- We factor the expression by grouping.
Let’s apply this method to the following examples.
Solution: Follow the steps outlined above.
The number 12 can be written as a product of two numbers in any of these ways:
The number 24 can be written as a product of two numbers in any of these ways.
Since -281 is much more negative than -43, you need to have a pair of factors where one is not so negative. Try:
This is close! Since it is still too negative, you need a factor that is less negative than -40, and one that is slightly more negative than -7. Try:
Sample explanations for some of the practice exercises below are available by viewing the following video. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. However, the practice exercise is the same in both. CK-12 Basic Algebra: Factor by Grouping and Factoring Completely (13:57)
Factor by grouping.