polynomial long division

Given two polynomialsPlanetmathPlanetmath a(x) and b(x) polynomial (long) division is a method for calculating a(x)/b(x) that is, finding the polynomials q(x) and r(x) such that a(x)=b(x)q(x)+r(x).

Here is an example to show the method.Let a(x)=x4-2x3+5 and b(x)=x2+3x-2. The method looks very similar to integer division since a polynomial i=0ncixi is somewhat similar to an integer i=0nci10i

In the initial setting we only write the coefficients, notice that a(x)=x4-2x3+0x2+0x+5. It will then be

In the next step we se that 1/1=1 and we multiply 1 3 -2 with 1 and then subtract the result.

Then we move down the next number, in this case a zero, and -5/1=-5 so we get -5, and multiply by -5 and subtract

as a final result we get

The result is q(x)=1-5 17, which translatesMathworldPlanetmath to q(x)=x2-5x+17 and r(x)=-61x+39.

It is also possible to write the entire polynomial, that is, writing all the xi’s. Like this

Title polynomial long division
Canonical name PolynomialLongDivision
Date of creation 2013-03-22 14:19:59
Last modified on 2013-03-22 14:19:59
Owner rm50 (10146)
Last modified by rm50 (10146)
Numerical id 7
Author rm50 (10146)
Entry type Definition
Classification msc 12D05
Related topic LongDivision