Have you ever been on a long trip and wished there was a short cut that could get you to your destination faster?
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
Well, that’s what this lesson is all about…
…a math shortcut!
Synthetic Division is a way for us to divide a polynomial of any degree by another polynomial quickly and easily, and without all the mess.
But to appreciate the beauty of Synthetic Division, we first have to remind ourselves of how we used to divide which is the process of Long Division.
Now, we’ve been successfully dividing using Long Division for years and years now, but when we start putting in variables, the process can be come tedious and, well, long!
Thankfully, there’s Synthetic Division!
As Purple Math nicely states, Synthetic Division is method for dividing by a linear factor (meaning the polynomial on the bottom is of degree 1), and shortens the process of dividing polynomials because there is less writing and calculations involved due to the fact that we are only going to be focusing on the coefficients rather than the variables and exponents.
Dividing Polynomials using Synthetic Division
In no time, we will see how straightforward this process is, and never look back.
But, did you know that there’s more! Not only are we getting a shortcut, but Synthetic Division can actually help us to evaluate polynomials!
Huh?
Yes, it’s true! Imagine that we have this really long and complicated polynomial, and you need to plug in a number and evaluate it. Ugh! Well, with the power of the Remainder Theorem (Synthetic Substitution) we can skip all the mess and get the answer we need without out too much work.
Awesome!
So, together we will learn:
- How to successfully use Synthetic Division to divide two polynomials.
- How to write our answers with a given remainder.
- Learn all about the Remainder Theorem and the power of Synthetic Substitution.
Synthetic Division (How-To) – Video
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