Solve Polynomial Division with Synthetic Division | Step-by-Step Guide

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Homework Help Overview

The discussion revolves around a polynomial division problem involving synthetic division, specifically the division of the polynomial \(6x^4-3x^3+5x^2+2x-6\) by \(3x^2-2\). Participants are exploring the methods and concepts related to synthetic division in this context.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the nature of synthetic division and its differences from traditional polynomial division. There is also discussion about the specific form of the divisor and its implications for the problem.

Discussion Status

The conversation includes attempts to clarify the concept of synthetic division and its applicability to the given problem. Some participants express uncertainty about the method's effectiveness due to the structure of the divisor, indicating a lack of consensus on how to proceed.

Contextual Notes

There is mention of the divisor not being in the form \(x - r\), which raises questions about the applicability of synthetic division. Additionally, the problem is noted as a homework assignment, which may impose certain constraints on the discussion.

Lucretius
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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.

[tex]\frac{6x^4-3x^3+5x^2+2x-6}{3x^2-2}[/tex]

The answer is [tex]2x^2-x+3[/tex]
 
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What is synthetic division and through what is it different from normal division?

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

Daniel.
 
dextercioby said:
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 [itex]x-r[/itex], but [itex]x^2-r[/itex] I haven't done it in a long time so I can't really help her with it.
 
It doesn't work,i'm afraid.You see,the denominator doesn't factor into monoms with integer ([itex]\in\mathbb{Z}[/itex]) roots,so the "trick" is useless.U might read better the Wiki page,if u don't trust me.

Daniel.
 

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