What if you had a polynomial expression like in which some of the terms shared a common factor but not all of them? How could you factor this expression? After completing this Concept, you'll be able to factor polynomials like this one by grouping.
Fisch Video: Factoring Polynomials by Grouping
Sometimes, we can factor a polynomial containing four or more terms by factoring common monomials from groups of terms. This method is called factor by grouping.
The next example illustrates how this process works.
There is no factor common to all the terms. However, the first two terms have a common factor of 2 and the last two terms have a common factor of . Factor 2 from the first two terms and factor from the last two terms:
Now we notice that the binomial is common to both terms. We factor the common binomial and get:
We factor 3x from the first two terms and factor 4 from the last two terms:
Now factor from both terms: .
Now the polynomial is factored completely.
Factor by grouping.
Additional Practice Opportunities (including self-check)
- Braingenie: Factoring Polynomials by Grouping Terms