Factoring by Grouping Worksheets
Factoring allows us to make sense of complex algebraic arrangements. Perhaps the most common method of factoring is to remove the greatest common factor between all the terms. When reviewing many different algebraic forms, you will come across terms that do not share a common factor at all. The next most common technique of factoring is called grouping. Grouping allows us to divide a set number of terms into a group of terms. In some cases, you may remove the greatest common factor and then employ this technique right after it. In other cases, you may group first and then remove common factors. In most cases, you can just separate the first half of the terms from the second half of the terms, but do not forget that can rearrange these expressions to make them work best for you. Often when we stuck somewhere along the way, it is best to start over and by rearrange the expression itself. These worksheets can be very helpful for learning to use the grouping technique.
Aligned Standard: 6.NS.B.4
- Step-by-Step Lesson- This lesson takes you through the two step process of: Step 1: Determine if all the four terms have anything in common between them. Does a greatest common factor (GCF) exist? In this case, all four terms only have 1 in common. This does not help us make progress. Step 2) We will start to approach the terms by grouping them together. If we consider the first two terms together and the last two terms together, we can make so progress.
- Guided Lesson - You will find which terms you can work off of and restate the expression in a simple form.
- Guided Lesson Explanation - This is where we start to split the expression into two parts.
- Basic Practice Worksheet - Factor each polynomial completely.
- Intermediate Level Worksheet - These problems are a bit more complex.
- Answer Keys - These are for all the unlocked materials above.
Each homework sheet helps you better understand the skill with a simple progression.
- Homework 1 - This is straight forward with minimal adjustments being needed to solve.
- Homework 2 - This allows you to work the skill in a skeleton like framework.
- Homework 3 - When you find the product of your solution, it should be what you started with.
- Homework 4 - We ramp up the front end terms here.
- Homework 5 - This gets a bit more complex and you will need to pull out multiple terms.
You will get another shot at these types on problems with more work on each successive version.
- Practice 1 - Make sure that you handle the exponents all the way through this one.
- Practice 2 - These may be a bit more complex for you to work with.
- Practice 3 - Start with the frontend term and then work your way back.
- Practice 4 - Locating the GCF is the flagship skill with this whole topic.
Math Skill Quizzes
This series of quizzes will help teachers and students see where they are lacking and where they have some strength.
- Quiz 1 - The most basic of skills are tested here.
- Quiz 2 - These questions would be aligned with a more intermediate level skill set.
- Quiz 3 - You might be hard pressed to determine the most core factors.
- Quiz 4 - Remember that you can pull out multiple factors in many of these problems.
How to Factor by Grouping
When we need to factor a polynomial, we are attempting to write it as a product of two or more polynomials. The grouping method of factoring is helpful when there is no common factor found among all of the terms. When we are factoring by grouping the equation should follow the standard format of: ax2 + bx + c. When you are certain that your equation fits this format, we can begin this process by:
Step 1: Product of Lead Coefficient and Constant - In the standard form of the equation (ax2 + bx + c) the leading coefficient is symbolized by the variable (a) and the constant is symbolized by the variable (c). We take the product of these variables (ac) to create what is called the master product.
Step 2: Break Master Product into Factors - Write all the factor pairs of the master product. We then evaluate all the pairs and compare them to variable (b). Identify the factor pair that has a sum equal to variable (b). Note: If the master product is a negative value, you will need to identify pairs that equal b when subtracted from one another.
Step 3: Separate the Center Term - The center term (bx) must be split into two terms. An easy way to do this is to create a sum of those values.
Step 4: Group in Pairs - Group the terms on the left into their own pair and do the same thing for the right.
Step 5: Factor Them - This means that you search for common factors of each pair and factor them out.