1. ## 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

2. Originally Posted by JonathanEyoon
(x^6 + x^4 + x^2 + 1) / (x^2 + 1)
$\displaystyle x^6+x^4+x^2+1=x^4(x^2+1)+(x^2+1)$

Does that make sense?

3. Originally Posted by Krizalid
$\displaystyle x^6+x^4+x^2+1=x^4(x^2+1)+(x^2+1)$

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?

4. 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 $\displaystyle y = x^2$. Then you wish to divide $\displaystyle y^3 + y^2 + y + 1$ by $\displaystyle y + 1$, 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 $\displaystyle y^2 + 1 = x^4 + 1$.

-Dan

5. Thanks alot guys.