Learning Objectives:

__Math Tutoring on Solving Quadratic Equations by Factoring__

A **"quadratic”** is a **polynomial** that looks like **ax² + bx + c,** where **a, b **and** c** are just numbers. The method for solving **quadratic equations by factoring** is based upon the **zero factor property** of real numbers. Here is what it says, “if two numbers, **a **and** b,** are multiplied together and the resulting product is **zero**, then at least one of the numbers must be **zero**.” So if we have **a x b = 0 **then** a = 0 **or **b = 0 **or** they both = 0. **Let us go ahead and apply this to **quadratic equations. **So all of these problems will be **factorable**, remember the first step in **factoring** is to look for the **greatest common factor** and there is a **common factor **of** x** here. So let us go ahead and **factor x **out. For the easy case of **factoring,** you will find two numbers that will not only multiply to equal the constant **term "c",** but also add up to equal **"b",** the coefficient on the **x-term**. In some cases, there is not a **GCF** for all the terms in a **polynomial**. If four terms have no **GCF**, then **factoring by grouping** is applied and following are the steps:

**Step 1: Group** the **first two terms** together and then the **last two terms **together.

**Step 2: Factor** out a** GCF** from each separate **binomial. **

**Step 3: Factor** out the common **binomial.**

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**Hook Questions:**

*1. **What is a quadratic equation?*

*2. **How do you solve a quadratic equation?*

*3. **How do you find the factors of an equation?*

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