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! 🙂
, and expanding them without a second thought. But what happens when our reliable squared binomials are now raised to the third power, such as,
? Luckily for us, there is a 
Example #2:
Practice Questions:
. This is a simple example, where we know the value of x is equal to 2,(
). But what if it were to get more complicated? That’s where logs come in!
But wait there’s more! Logs have a certain set of 
We can use these rules to help us algebraically solve logarithmic equations, let’s look at an example that applies the Product Rule.
Example: Solve the following algebraic equation below for the missing variable (aka, solve for x).
Explanation:
Therefore we also know that if we raise the entire radical expression to the same power of the root, the two exponents will cancel each other out:
When you’re ready, check out the below:
Explanation:
to our quotient! We just put the remainder over the divisor to represent this extra bit of solution.
When you’re ready, check out the 
!
