## An interesting way to divide polynomials.

Along with coding languages, I’ve been learning algebra by myslef. Since soding langyuages have soimething to do with algebra, it’s always beneeficial for me to keep interacting with numbers and the mathmatical.logical way of thnking.

Let’s talk about algebra this time. I’ve been lately re-learning algebra from scratch, and because of the time restrictions, I can’t share everything I learn there. But I’d like to share at least those that caught my attention and want to take some notes not only for myself but for those who might be curious about it.

This time is about dividing polynomials. Adding, subtracting, and multiplying polynomials are kind of easy. But when ito comes to divisions, the story is a little different since the way we calculate it is a bit complex form the rest.

Here, I used my newly bought Samsung Galaxy Tab S8+ to explain how the mechanism works. Let’s dive into it!!

First of all, this is the completed one.

From here, step by step, let me explain how things work. Remember, last time, I mentioned the consecutive numbers, right? Here, we can take advantage of the method. In this case, we have x³ + 2x² + 12. So, what we miss is an x in between 2x² and 12. So, convert it to x³ + 2x² + 0x + 12

Once you converted it to calculatable format, just make it into a dividable format like the below image.

From here, we start divisions. First of all, think what makes the x into x³ by multiplying. In this case, it’s x², so white it down on top of it.

Then, multiply x- 1 by x² individually. You wi;; have x³ – 3².

Then subtracting them. Remember, negative x negative -> positive; so the second negative sign is turned to positive. Now you have 3x².

Now, drop the 0x to that point.

Just repeat what we did a while ago. Just multiply x – I by 3x individually. Now we have 3x² – 3x.

Drop the 12.

Repeat the process again.

The same thing. Negative x negative -> positive. Now we get 15.

So the final answer is x² + 3x + 3 + 15/x -1.

So, did you like it? I personally enjoyed the process of it because it’s simply a little different from other polynomial calculations. I’ll keep up to date about my algebra journey, so hope you’ll enjoy your own as well. Keep learning, keep growing, and keep smiling.

Happy learning!!