Algebra - Dividing Polynomials with Remainders

[Michael Phillips]

How on the Nspire CAS would I solve a division of a polynomial with a remainder without it giving me a weird answer

--
Michael H Phillips
Senior - 2009 - MSHS
Arlington, Texas

[Piman]

I guess it depends on what you mean by a weird answer.

Let P(x) = the polynomial
D(x) = the divisor
R(x) = the remainder
Q(x) = the quotient

Use PropFrac(P(x)/D(x)), and you get the answer in the form:

R(x)/D(x) + Q(x)

This is similar to writing a numerical result of 30/7 as 2/7 + 4
instead of 4 r2.

Marc Garneau

On Jan 27, 9:03 am, Michael Phillips <michaelhphill...@gmail.com>
wrote:

[Nelson Sousa]

and to do it the other way around use "comdenom".

A note on the propfrac function applied to polynomials: on 1 variable polynomials there's no ambiguity, but on polynomials on several variables, there's always the matter of the ordering of the terms, in order to apply the division algorithms. The Nspire CAS (as well as other CAS calculators) uses the somewhat standard LEX ordering, meaning that terms are ordered first by the degree of the variable that appears first on the alphabetical ordering. So, if your variables are x, y and z, the following terms will appear in this order:

x^3 y + x^2 y^2 + x^2 y + x^2 z^2 + x y^5, etc.

The relevance of this is that the result of the division is different, depending on the order you choose.

More about this: http://www.geocities.com/famancin/orderings.html

More about polynomial division and the problems that can arise related to the choice of order: http://en.wikipedia.org/wiki/Multivariate_division_algorithm

Nelson

[Sean Bird]

I like the methods proposed.

With TI-Nspire CAS, under MENU > Algebra > there are also polynomial features.
e.g.
  polyQuotient(x^3+3x^2+5,−2x+1)