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Factoring by Grouping

Use associative and commutative properties with factoring

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Factoring by Grouping

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

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CK-12 Foundation: 0913S Factoring By Grouping

Guidance

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.

Example A

Factor .

Solution

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:

Example B

Factor .

Solution

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.

Practice

Factor by grouping.

Additional Practice Opportunities (including self-check)

  1. Braingenie: Factoring Polynomials by Grouping Terms

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