![]() The standard approach of starting with the highest degree terms ensures that if you end up with a remainder, its degree will be less than the degree of the divisor, but also means that you can only divide when the degree of the divisor is less than the dividend. The method illustrated above is sometimes called the "reverse tabular" method ("reverse" because using a table in the normal fashion of filling in the interior given the top row and left column is used for multiplying polynomials). The rest of this example can be found in a more helpful post. In the example below, we look at the 3 x term and ask how many times does it go into the 9 x^3 term - the answer is 3 x^2, which is the first term of our answer. This tells you the first term of your quotient q. When you divide single-variable polynomials f / g, the standard ( euclidean) algorithm requires f to have a higher degree than g, and when you start dividing you take the term of the highest power of g and see what you should multiply that by to get the term with the highest power in f. ![]() If you are intrigued by the possibility of polynomial explosions, read on for others: you've been warned. Specifically, if you divide in a "backwards" fashion, things can blow up spectacularly. The current post shows some surprising things that happen when you mess around with the standard division algorithm, and is probably not quite as helpful. ![]() Among the Lakota people, the heyoka is a contrarian, jester, satirist or sacred clown. The heyoka speaks, moves and reacts in an opposite fashion to the people around them. - Wikipedia, HeyokaĪ couple of earlier posts ( this one and this one) describe how to use the grid method for dividing polynomials, and were intended to be helpful for people learning or teaching the topic.
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