Learning Objectives:

__Math Tutoring on Determining the Greatest Common Factor and Factoring by Grouping__

**Factoring** is a technique that is often useful when trying to solve polynomial equations algebraically. The **GCF** is the largest monomial that divides or is a **factor** of each term of the polynomial. To **factor** an expression means to write an equivalent form that is a product. The first step in **factoring** is always to look for **factors **common in every term to identify the **largest or greatest common factor**. Then we use a distributive property to **factor** out the **GCF **and write the polynomial as a product. **Factor **by grouping technique can be useful when there is a **binomial factor** of a polynomial with four or more terms. To **factor** **by grouping **following steps are followed in math tutoring:

1. We divide the polynomial into two groups, the first half, and the second half.

** **2. We **factor** the **GCF** out of the first half and then** factor** the **GCF** out of the second half.

3. We should notice a common **binomial or trinomial factor**, depending on how many terms we started with.

4. We **factor** out the common **binomial or trinomial factor**.

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**Hook Questions:**

*1. **What does it mean to factor by grouping?*

*2. **How do you factor out the GCF from a polynomial?*

*3. **How do you use the GCF when factoring a 4 term polynomial by grouping?*

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