# Factoring Completely

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## Objective

Students will be able to factor polynomials completely.

#### Big Idea

Multiple methods for finding the factors of polynomials are addressed and analyzed in this lesson.

## Warm up and Homework Review

10 minutes

I include Warm ups with a Rubric as part of my daily routine.  My goal is to allow students to work on Math Practice 3 each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. The Video Narrative specifically explains this lesson’s Warm Up- Factoring Completely which asks students to determine which of two answers is the proper factored form of a polynomial.

I also use this time to correct and record any past Homework.

## Intro to Factoring Completely

7 minutes

I begin this lesson with the polynomial 2x2 + 6x + 4.  The students are going to factor this problem.  They get either (2x+2)(x+2) or (x+1)(2x+4).  I get a volunteer to share their answer and then ask if everyone got that solution.  Someone else shares the other factored form or, given a shy class, I note that I saw the second form on someone’s paper.  I ask if they are both correct or if one is a mistake.  The students will check and see that they are both correct.  I then ask WHY (Math Practice 7).  One of the students should note that there is a factor of two which means is can also be factored as 2(x+1)(x+2).  I ask which form is best.  This leads us to the fact that our new rule is that you always look for a greatest common factor first.

## Create a Diagram

15 minutes

As pairs, students come up with a list of the types of factoring that we have talked about as well as their traits.  This list gets discussed as a class.

I then ask them to create their own flow chart or diagram describing what type of factoring to use given a polynomial.  This is the key activity of the day.  Students need to be able to take any polynomial and factor it without specific directions on which technique to use.  Rather than making a chart FOR the students, they make one for themselves (Math Practice 7).  I have them work individually checking with their partner as needed for feedback.  They then get together with another pair and each person share’s their chart.  They select the best chart of the four and that person gets to share his/her chart describe and why it was chosen with the class.

## Guided Practice

15 minutes

The remainder of the lesson is Guided Practice.  This gives the students an opportunity to use the diagrams that they created to factor these appropriately (Math Practice 5).  I verbally model how to use their diagram in the beginning extending to having students explain to each other as we progress.

## Exit Ticket

3 minutes

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.

Today's Exit Ticket asks students to completely factor a polynomial.

## Homework

This Assignment allows students to practice using all the factoring skills together.  These are eight of these types of problems.  The final two problems are extension problems (Math Practice 1).  Rather than a single variable, these problems must be factored using an expression.