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 Skip Navigation LinksMath Help > Procedures > Polynomial Division

Polynomial Division is a way of "dividing" one polynomial by another, resulting in a quotient and a remainder, both of which are polynomials.  Given f(x) and g(x), where the degree of f is higher than the degree of g, the procedure divides f(x) by g(x), resulting in a quotient q(x) and remainder r(x) such that

q(x) g(x) + r(x) = f(x)

Another way to express this, which makes it clearer that we're dividing f(x) by g(x) is:

f(x)/g(x) = q(x) + r(x)/g(x)

 . . . . . .  This page is a work in progress; Still to do: check the Internet Reference, add more of an algorithm to this page, and see if you can add one more example.  The divisor need not be monic, so the quotient might have rational (as opposed to integral) coefficients.  Also, check all the pages that refer to Synthetic Division to see if they more properly should refer to Polynomial Division, and fix 'em up.

Here's an example of a polynomial division problem:

         2x² -3x  +6 
   -----------------
x+4)2x³ +5x² -6x +31
    2x³ +8x² 
    --------
        -3x² -6x
        -3x²-12x
         -------
              6x +31
              6x +24
              ------
                   7

The final answer, then is:

(2x³+5x²-6x+31)/(x+4) =

2x²-3x+6 + 7/(x+4)

Internet references

For a tutorial explaining division of polynomials, see http://sosmath.com/algebra/factor/fac01/fac01.html

Wikipedia: Polynomial long division

Related pages in this website

Back to Word Problems

Synthetic Division

Polynomial Remainder Theorem

Polynomial

 

The webmaster and author of this Math Help site is Graeme McRae.