Algebra II : Unit #3 - Polynomials : Lesson #7

Factoring Trinomials

Objective: Students will be able to factor quadratic trinomials.
Standards: HSA-SSE.A.2 MP1 MP3 MP5 MP7
Subject(s): Math
60 minutes
1 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 homogenous pairs provides an opportunity for appropriately differentiated math conversations. The Video Narrative specifically explains this lesson’s Warm Up- Factoring Trinomials which asks students to determine which fictitious student properly factored a polynomial.

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

2 Factoring Trinomials Graphically - 13 minutes

My students have not yet factored trinomials this year.  Most of them haven’t seen them for two years. This skill is important to the success of my students in the Common Core Algebra 2 standards.   Please watch my Video for more information on my reasoning for reviewing factoring. 

We are going to begin by looking at factoring graphically.  It is important to remind them that a quadratic is a product of two linear functions which we call the factors.  I give my students the graph and equation: f(x) = x2 + 2x – 15 and ask them to identify the factors from the graph.   This problem should be pretty straight forward as they did similar problems in the previous lesson.  I give the students a chance to find the factors and then we go over it as a class.

The next quadratic function that I give the students to factor graphically is f(x) = 2x2 - x – 2.  This problem is slightly more involved as the students will get (x – 2)(x + ½).  Once they get to this point, I show them how it doesn’t factor to the original function.  I tell them it is a correct factoring however and then ask them to discuss with their partner why it is correct even if it doesn’t distribute to our original function (Math Practice 7).  We talk about it as a class and hopefully some groups have a decent understanding as to why.  If not, I will refer them back to the slide from the previous lesson where there were four functions with the same roots that are all multiples of each other.  This is actually a multiple of x2 – 1/2x – 1.

The final graph we look at is for f(x) = x2 + 4x + 4.  I give this problem to my students with no introduction (Math Practice 1).  This may get stuck that x + 2 seems to be the only factor.  Once they have had a chance to look at this, if they seem to be struggling, I’ll give them the hint that all of the other functions when through the x-axis while this one touches in and goes back up.  The goal is that the students will connect that there are two factors in the same place and this is how it is reflected in the graph. 

To conclude this section, I ask the students to identify the strengths and weaknesses of this method of factoring(Math Practice 5).  This knowledge will build as we get deeper into the study of polynomials but it is still important to keep them thinking about these things as we go along.  

3 Factoring Trinomials Algebraically - 20 minutes

I have a method for teaching trinomials that allows students to factor a polynomial with a leading coefficient larger than one as easily as factoring one without.  Please watch my video for more information.  As with any other skill in my class, I do not insist that students use a specific method.  My only request is that whatever method they use is efficient and accurate.  The rest of this lesson involves Guided Practice.  I have purposefully not addressed quadratics that are not factorable as this will be the central discussion for the next lesson.  

4 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 factor a trinomial.

5 Homework - 0 minutes

The first two problems in this assignment ask the students to find the factors of quadratics graphically.  The next eight are practice problems to solidify the skill of factoring trinomials.  The final problem asks the students to compare and contrast for each method of factoring trinomials (Math Practice 5).   

This assignment was created using Kuta Software, a product I would highly recommend to any mathematics teacher.