The idea is to work the distributive property in reverse. The goal is to write polynomials as products of simpler polynomials.

*x*and

*y*.

**Identify the GCF**.

**Factor out the GCF**:

**Step 1**: Identify the GCF.

**Step 2**: Divide each term by the GCF to determine the remaining factor.

**Step 3**: Check by multiplying.

**Factor the GCF out of the expression**.

**Tip**: Be careful to use a 1 when the entire term factors out. This is where a mental check is important. Be sure that if you were to distribute you would get back to the original expression.

**Factoring 4-Term Polynomials by Grouping**

Now we will use the idea of factoring out the GCF in a technique called factoring by grouping of four-term polynomials. The steps are as follows.

**Factor**:

**Step 1**: Group the first two terms and the last two terms. Factor out the GCF of both groupings.

**Step 2**: If the remaining binomial factors are the same factor it out.

**Step 3**: Check by multiplying.

**Factor by grouping**.

**Video Examples on YouTube**: