Homework Help: Synthetic Division

1. Apr 13, 2005

Lucretius

I was wondering if you could help me out with this problem. Please explain how to solve using synthetic division. I need to know how to solve it.

$$\frac{6x^4-3x^3+5x^2+2x-6}{3x^2-2}$$

The answer is $$2x^2-x+3$$

2. Apr 13, 2005

dextercioby

What is synthetic division and through what is it different from normal division?

Daniel.

3. Apr 13, 2005

Lucretius

Synthetic Division is described here. It's a faster way of doing polynomial division.

4. Apr 13, 2005

dextercioby

AAAaaaaaaaaaaaaah,i knew it under the name "Schema lui Horner" (Horner's trick).Well,wasn't that Wiki page clear??

Daniel.

5. Apr 13, 2005

Lucretius

This is actually a homework problem my sister posted (shes in alg/trig). What she is getting stuck on is the fact that the bottom is not $x-r$, but $x^2-r$ I haven't done it in a long time so I can't really help her with it.

6. Apr 13, 2005

dextercioby

It doesn't work,i'm afraid.You see,the denominator doesn't factor into monoms with integer ($\in\mathbb{Z}$) roots,so the "trick" is useless.U might read better the Wiki page,if u don't trust me.

Daniel.