Polynomial Inequalities

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Students will be able to find the solution to a polynomial inequality.

Big Idea

Students explore polynomial inequalities algebraically and graphically.

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. To prepare students for the lesson. this warm up has students refresh what they know about linear inequalities by as they determine whether or not the problem presented has been solved correctly. Please watch my Video Narrative for more information.

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

Solving Polynomial Inequalities Graphically

20 minutes

This introductory lesson is an extension that goes beyond the topics required in Algebra 2 by the Common Core.  It is in no way exhaustive of this topic but instead gives students a conceptual starting place.

I chose to start this lesson graphically to lay the conceptual groundwork for polynomial inequalities.  My students are already familiar with solving linear inequalities graphically so this idea isn't new.  This will help them see why the solution may be more than one interval.  

This lesson begins with the inequality: x2 – 1 > x + 5.  The first thing the students do is graph each side of this inequality using their graphing calculator.  I ask them to locate the solution and we verbalize the solution.  I then have them write the solution using interval notation and graph it on a number line.  All inequalities we solve will be represented both of these ways.  Next, I have them rewrite this inequality into equivalent forms, like x2 > x + 6, which we make a list of on the board, and they choose one or two to graph on their calculator.  They will quickly see that they get the same solution no matter which form we use (Math Practice 7).  We will then do a think-pair-share discussing which form made it the easiest to find the solution (Math Practice 5).  Next, I will give them the same inequality with a switched sign. 

There are several more polynomial inequalities for the students to solve graphically.  Each one provides students with a slightly different variation.  Specifics about these inequalities are located in the PowerPoint.  

Solving Polynomial Inequalities Algebraically

18 minutes

Now that the students have a good idea of what the solutions to these types of equations look like, we will solve them Algebraically.  I begin with the original problem x2 – 1 > x + 5 and model its solution.   We then do Guided Practice on several more problems including the ones we solved graphically. 

As we go through this, I ask the students to think about why we would use this method rather than the graphing method.  

Exit Ticket

2 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 find the solution to a polynomial inequality.


This Assignment has two polynomial inequalities to be solved graphically and six to be solved graphically.  The goal of this section is to reinforce the skills learned in the day's lesson.  It ends by asking the students to identify with method they prefer and why (Math Practice 5).  

This assignment was created with Kuta Software, an amazing resource for mathematics teachers.