factoring-a-trinomial-with-a-lead-coefficient-not-1

Welcome to Clip from Spiral logo

Interactive video lesson plan for: Factoring a trinomial with a lead coefficient not 1

Activity overview:

Factoring a trinomial with a lead coefficient, not one, resources.
http://www.moomoomathblog.com/2017/02/factoring-trinomial-with-lead_6.html
In Algebra a trinomial is a polynomial with three terms. Use this method I call the "rainbow method" to help with your factoring.

This rainbow method works great with a trinomial with a led coefficient greater than one, and there is not a greatest common factor.
Example problem 1 Factor 6x^2 +7x -5
Example problem 2 Factor 15x^2 + 17x -4

Hi welcome to MooMooMath Today we are going to look at factoring a trinomial that has a lead coefficient that is not one. I call this the rainbow method. It will help if you know how to factor by grouping, but if you don't it is ok, but we use factor by grouping and it is helpful if you know it.
The first thing we need to do is identify which trinomials we can use the rainbow method with. If our lead coefficient is greater than one (in this example it is a 6) and there is not a greatest common factor, then it is a great time to use the rainbow method. To use the rainbow method I'm going to take a because this is in standard form Let,s write our standard form so you can see it. I will multiply a times c, and see how I wrote it over top. This is why it is the rainbow method. Take time c and you get negative 30. Next, ask yourself what multiplies to negative 30, middle term but adds to the middle term. Our middle term b is positive 7. So we are looking for two values that multiply to negative 30 but add to 7. So let's find some combination. 1x30 no,2x15,no 3 times 10. Yes. Here is a combination that multiplies together to equal 30 and adds to positive 7. So the signs will be 3 and 10 are the two numbers, and the sign is negative so the three must be negative to get the 30. Now what I will do is take the two factors, middle term, the 7x and split it into two parts. A negative 3x +10x I 'm rewriting the middle term to be two different terms which are the sum of the two required factors. I will then bring down my a squared which is 6x^2. I then will bring down my c which is negative 5. The front term and the back term remain the same. Now I will factor by grouping because I have four terms. Factor the first two terms together, and the last two terms together. When I do this I will take the greatest common factor out of the first two terms which are 3x , and I left with 2x minus 1. I will do the same to the back. What is my common factor? 5 I will factor with positive 5 and I'm left with (2x -1) Now what is nice about factoring by grouping is that you can see these two factors need to match and they do. I will now factor the (2x-1) out. I will take the (2x-1) out of both terms, and when I do I'm left with (3x +5.) And there is how I factor by grouping. Lets do one more of those. 15x^2 + 17x -4
Does it qualify, yes the first term is greater than 1, and there is not a greatest common factor? Multiply the first term by the last term. 15 times 4 = 60. Next, what multiplies together to equal 60, but adds together to equal the middle term. 3 times 20 equals 60, and when you subtract 20-3 they equal the middle term. The 20 has to be positive, and the 3 has to be negative. Let's split the middle number to be -3x plus 20x. The order I write these down doesn't matter. Bring down c and bring down an x squared. Now factor by grouping. Group the first two together. What is my common factor? 3x is my common factor. I'm left with (5x -1) What is common in the back? 4 is common and I'm left with (5x-1). Do my binomials match? Yes, Factor out this binomial (5x-1) and we are left with (5x-1)(3x+4) I hope this rainbow method has been helpful when your lead coefficient is not one.

-~-~~-~~~-~~-~-
Please watch: "Study Skills Teacher's Secret Guide to your Best Grades"
https://www.youtube.com/watch?v=f3bsg8gaSbw
-~-~~-~~~-~~-~-

Tagged under: Trinomial,Algebra (Field Of Study),factoring,trinomials,factor grouping,factoring polynomials,algebra,Factorization (Literature Subject)

Clip makes it super easy to turn any public video into a formative assessment activity in your classroom.

Add multiple choice quizzes, questions and browse hundreds of approved, video lesson ideas for Clip

Make YouTube one of your teaching aids - Works perfectly with lesson micro-teaching plans

Play this activity

1. Students enter a simple code

2. You play the video

3. The students comment

4. You review and reflect

* Whiteboard required for teacher-paced activities

Share on:

Share Factoring a trinomial with a lead coefficient not 1 on Google+ Share Factoring a trinomial with a lead coefficient not 1 on Twitter Share Factoring a trinomial with a lead coefficient not 1 on Facebook Pin Factoring a trinomial with a lead coefficient not 1 Email Factoring a trinomial with a lead coefficient not 1

Ready to see what else Spiral logo can do?

With four apps, each designed around existing classroom activities, Spiral gives you the power to do formative assessment with anything you teach.

Quickfire

Carry out a quickfire formative assessment to see what the whole class is thinking

Discuss

Create interactive presentations to spark creativity in class

Team Up

Student teams can create and share collaborative presentations from linked devices

Clip

Turn any public video into a live chat with questions and quizzes

1000s of teachers use Spiral to deliver awesome, engaging activities that capture students' understanding during lessons.

Now it's your turn Sign up

Spiral Reviews by Teachers and Digital Learning Coaches

Spiral
Review of Spiral by teacher: Kathryn Laster @kklaster

Tried out the canvas response option on @SpiralEducation & it's so awesome! Add text or drawings AND annotate an image! #R10tech

Spiral
Review of Spiral by teacher: Room 220 Math Stars @3rdgradeBCE

Using @SpiralEducation in class for math review. Student approved! Thumbs up! Thanks.

Spiral
Review of Spiral by teacher: Miss Ord @ordmiss

Absolutely amazing collaboration from year 10 today. 100% engagement and constant smiles from all #lovetsla #spiral

Spiral
Review of Spiral by teacher: Adam J. Stryker @strykerstennis

Students show better Interpersonal Writing skills than Speaking via @SpiralEducation Great #data #langchat folks!

Spiral
Review of Spiral by teacher: Dr Ayla Göl @iladylayla

A good tool for supporting active #learning.

Spiral
Review of Spiral by teacher: Brett Erenberg @BrettErenberg

The Team Up app is unlike anything I have ever seen. You left NOTHING out! So impressed!

Get the Clip Chrome Extension & Create Video Lessons in Seconds

Add Clip to Chrome