Algebra 2: Synthetic Division and Factoring Polynomials

Hey there math friends! In this post we will go over how and when to use synthetic division to factor polynomials! So far, in algebra we have gotten used to factoring polynomials with variables raised to the second power, but this post explores how to factor polynomials with variables raised to the third degree and beyond!

If you have any questions don’t hesitate to comment or check out the video below. Also, don’t forget to master your skills with the practice questions at the end of this post. Happy calculating! 🙂

What is Synthetic Division?

Synthetic Division is a shortcut that allows us to easily divide polynomials as opposed to using the long division method.

When can we use Synthetic Division?

We can only use synthetic division when we divide a polynomial by a binomial in the form of (x-c), where c is a constant number.

Check out the Example below to see synthetic division in action:

Synthetic Division can also be used when Factoring Polynomials!

Let’s take a look at the following example and use synthetic division to factor the given polynomial:

Check!

Try the practice problems on your own below!

Still got questions? No problem! Don’t hesitate to comment with any questions or check out the video above. Happy calculating! 🙂

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Algebra 2: Expanding Cubed Binomials

Greetings math friends! This post will go over how to expand and simplify cubed binomials 2 different ways. We’re so used to seeing squared binomials such as, Screen Shot 2020-08-19 at 11.29.14 AM.png, and expanding them without a second thought.  But what happens when our reliable squared binomials are now raised to the third power, such as,Screen Shot 2020-08-19 at 11.29.48 AM?  Luckily for us, there is a Rule we can use:

Screen Shot 2020-08-18 at 10.12.33 PM

But where did this rule come from?  And how can we so blindly trust it? Which is why we are going to prove the above rule here and now using 2 different methods:Screen Shot 2020-08-19 at 11.31.13 AM

Why bother? Proving this rule will allow us to expand and simplify any cubic binomial given to us in the future! And since we are proving it 2 different ways, you can choose the method that best works for you.

Method #1: The Box MethodScreen Shot 2020-08-18 at 10.14.37 PMScreen Shot 2020-08-18 at 10.14.55 PM.pngScreen Shot 2020-08-18 at 10.15.06 PMScreen Shot 2020-08-18 at 10.15.39 PM.pngScreen Shot 2020-08-18 at 10.15.50 PM

Screen Shot 2020-08-19 at 2.24.54 PMScreen Shot 2020-08-19 at 2.53.43 PM

Screen Shot 2020-08-19 at 2.29.22 PM.pngScreen Shot 2020-08-18 at 10.17.19 PM.png

Screen Shot 2020-08-19 at 2.27.56 PMScreen Shot 2020-08-19 at 2.54.36 PM.png

Screen Shot 2020-08-18 at 10.21.05 PM.png

Method #2: The Distribution MethodScreen Shot 2020-08-18 at 10.17.54 PM.pngScreen Shot 2020-08-18 at 10.19.49 PMScreen Shot 2020-08-19 at 2.42.11 PM

Screen Shot 2020-08-18 at 10.21.05 PM.png

Now that we’ve gone over 2 different methods of cubic binomial expansion, try the following practice questions on your own using your favorite method!

Practice Questions: Expand and simplify the following.

Screen Shot 2020-08-18 at 10.21.56 PM

Solutions:

Screen Shot 2020-08-18 at 10.22.19 PM.png

Still, got questions?  No problem! Check out the video above or comment below! Happy calculating! 🙂

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**Bonus: Test your skills with this Regents question on Binomial Cubic Expansion!

 

Algebra: 4 Ways to Factor Quadratic Equations

*If you haven’t done so, check out the video that goes over this exact problem, and don’t forget to subscribe!

Screen Shot 2020-06-02 at 3.03.55 PMScreen Shot 2020-06-02 at 3.04.24 PM____________________________________________________________________Screen Shot 2020-06-02 at 3.20.04 PM____________________________________________________________________

Screen Shot 2020-06-02 at 3.07.02 PM____________________________________________________________________
Screen Shot 2020-06-02 at 3.07.42 PM
Choose the factoring method that works best for you and try the practice problems on your own below!

Practice Questions:

Screen Shot 2020-06-02 at 3.09.58 PMSolutions:

Screen Shot 2020-06-02 at 3.10.30 PM

Want a review of all the different factoring methods out there?  Check out the ones left out here (DOTS and GCF) and happy calculating! 🙂

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