Dividing 6x^4 - 3x^3 + 5x^2 + 2x - 6 by 3x^2 - 2

[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 $$2x^2-x+3$$

 

[dextercioby]

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

Daniel.

 

[Lucretius]

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

Daniel.

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

 

[dextercioby]

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

Daniel.

 

[Lucretius]

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

Daniel.

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.

 

[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.