# Dividing Polynomials

• Sep 8th 2007, 09:08 AM
JonathanEyoon
Dividing Polynomials
I know how to do the long division method but i'm a bit lost with the synthetic way. What are the rules and method in doing it this way?

An example to use

(x^6 + x^4 + x^2 + 1) / (x^2 + 1)

Thanks alot
• Sep 8th 2007, 09:17 AM
Krizalid
Quote:

Originally Posted by JonathanEyoon
(x^6 + x^4 + x^2 + 1) / (x^2 + 1)

$x^6+x^4+x^2+1=x^4(x^2+1)+(x^2+1)$

Does that make sense?
• Sep 8th 2007, 09:37 AM
JonathanEyoon
Quote:

Originally Posted by Krizalid
$x^6+x^4+x^2+1=x^4(x^2+1)+(x^2+1)$

Does that make sense?

yea but isn't that just factoring out? Or does it have something to do with dividing by means of the synthetic method? :confused:
• Sep 8th 2007, 02:30 PM
topsquark
Quote:

Originally Posted by JonathanEyoon
I know how to do the long division method but i'm a bit lost with the synthetic way. What are the rules and method in doing it this way?

An example to use

(x^6 + x^4 + x^2 + 1) / (x^2 + 1)

Thanks alot

You can't do synthetic division unless you are dividing by a linear polynomial.

So in this case, let $y = x^2$. Then you wish to divide $y^3 + y^2 + y + 1$ by $y + 1$, which is a problem you can do synthetically:
Code:

```-1 | 1  1  1  1   |    -1  0  -1     1  0  1  |0```
So the result is $y^2 + 1 = x^4 + 1$.

-Dan
• Sep 8th 2007, 04:31 PM
JonathanEyoon
Thanks alot guys.