To create this article, 129 people, some anonymous, worked to edit and improve it over time. This process is an easy one to learn, and the ability to do long division will help you sharpen your understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.
Regardless of whether a particular division will have a non-zero remainder, this method will always give the right value for what you need on top.
In this way, polynomial long division is easier than numerical long division, where you had to guess-n-check to figure out what went on top.
So let's say I want to divide-- I am looking to divide 3 into 43.
And, once again, this is larger than 3 times 10 or 3 times 12.
Let's now see if we can divide into larger numbers. But it doesn't go into it cleanly because 7 times 3 is 21. So if you take 23 minus 21, you have a remainder of 2.
And just as a starting point, in order to divide into larger numbers, you at least need to know your multiplication tables from the 1-multiplication tables all the way to, at least, the 10-multiplication. So you could write that 23 divided by 3 is equal to 7 remainder-- maybe I'll just, well, write the whole word out --remainder 2. So 4 goes into 34-- 30-- 9 is too many times, right?
If you're dividing a polynomial by something more complicated than just a simple monomial (that is, by something more complicated than a one-term polynomial), then you'll need to use a different method for the simplification.
That method is called "long polynomial division", and it works just like the long (numerical) division you did back in elementary school, except that now you're dividing with variables.
And, at least when I was in school, we learned through 12 times 12. Let's say I'm taking 25 and I want to divide it by 5. But for now, you just say, well it goes in cleanly 7 times, but that only gets us to 21. So you can even work with the division problems where it's not exactly a multiple of the number that you're dividing into the larger number.
So I could draw 25 objects and then divide them into groups of 5 or divide them into 5 groups and see how many elements are in each group. Well you say, that's like saying 7 times what-- you could even, instead of a question mark, you could put a blank there --7 times what is equal to 49? But let's do some practice with even larger numbers. So let's do 4 going into-- I'm going to pick a pretty large number here --344. This is way out of bounds of what I know in my 4-multiplication tables.