What if There is No Common Factor?

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SWBAT factor a polynomial expression made up of four terms with no GCF.

Big Idea

The factoring by grouping strategy is used to get students thinking about factoring an expression into two binomials.


5 minutes

My plan is to use the think pair share strategy to meet my goals for this launch. I begin class by letting students think about the question posed on the factoring_polynomials_grouping slide independently.

As students begin to put down some ideas, I will make my way around the room to observe.  I am looking for students who are making a connection to the idea that the factors must multiply to obtain the original expression.  

Once students have had a couple of minutes to think independently, I let them pair up and discuss their ideas with a partner.  Listen for students that are making sense of the problem and ask one or two pairs to share their reasoning with the class (MP3).

Teaching Note: I also discuss this opening in the beginning of the direct instruction portion of this lesson.

Direct Instruction

10 minutes

I prepared this video to introduce the factoring_polynomials_grouping_direct worksheet.  I plan to use a gradual release as we progress through this series of questions.  In the first example, I will do the entire problem with students.  In the second example, I will help students with the procedure of factoring out the gcf from the first row and then let them finish factoring.  In the third example, I hope to be able to allow my students to work independently.



20 minutes

For practice today, I will ask students to work with their partner on this practice activity from kutasoftware.com: factoring_polynomials_grouping_practice.  

As they work on the worksheet, I will encourage my students to use an area model to structure the expression and then determine two binomial factors.  Depending on the amount of time available, I will choose which practice problems to assign to students.  

Today, I plan to have my students choose any eight problems and factor them into two binomials using the area model.  I plan to post the answer key so that as students are working they can independently check their work.  I also encourage students to check their work by multiplying the binomial factors to ensure their factors make sense (MP3).

Teaching Note: Some of the expressions require students to factor completely.  This means that one or both of their binomial factors will have a greatest common factor that can be factored out.  Some students will notice this but others may not.  Don't be too concerned if students are not factoring completely as this will be addressed both in the closing of this lesson and in future lessons.


5 minutes

To close today's lesson, I will ask students to complete factoring_polynomials_grouping_close as a Ticket out the Door. I will ask my students to record their response on a half sheet of paper.


In question Number 1, students will look at the structure (MP7) of the binomials factors to determine if they are factored completely (aka, are they both prime factors).  I want my students to notice that 4x and 8 have a common factor of 4.  In the second part of the question, I am trying to assess students' understanding of the connection between factors and the original expression. Again, I hope students realize that to find the original expression they need to multiply the factors.

I hope that by asking students to think in both directions (multiplying and factoring), I will help them to see the connection and gain deeper conceptual understanding of polynomial expressions.