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

  • Thread starter Thread starter Lucretius
  • Start date Start date
  • Tags Tags
    Division
Click For Summary
SUMMARY

This discussion focuses on solving polynomial division using synthetic division, specifically the example of dividing \(6x^4-3x^3+5x^2+2x-6\) by \(3x^2-2\). The result of this division is \(2x^2-x+3\). Synthetic division is identified as a faster method for polynomial division, also known as Horner's method. The conversation highlights the limitations of synthetic division when the denominator does not factor into monomials with integer roots.

PREREQUISITES
  • Understanding of polynomial functions and their degrees
  • Familiarity with synthetic division techniques
  • Knowledge of Horner's method for polynomial evaluation
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the process of synthetic division in detail
  • Learn about Horner's method and its applications in polynomial evaluation
  • Explore polynomial long division for comparison with synthetic division
  • Investigate the conditions under which synthetic division is applicable
USEFUL FOR

Students studying algebra and trigonometry, educators teaching polynomial division methods, and anyone looking to improve their understanding of synthetic division techniques.

Lucretius
Messages
151
Reaction score
0
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
 
Physics news on Phys.org
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 x-r, but x^2-r 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 (\in\mathbb{Z}) roots,so the "trick" is useless.U might read better the Wiki page,if u don't trust me.

Daniel.
 

Similar threads

MHB Finding the Largest Root of a Polynomial Using Synthetic Division
  • · Replies 1 ·
Replies
1
Views
1K
P.S. I did it on paperPolynomial Division: 3x^3-5x^2+10x+4 / 3x+1
  • · Replies 2 ·
Replies
2
Views
2K
MHB Is x+1 a Factor of the Polynomial x^3-5x^2+3x+1?
  • · Replies 2 ·
Replies
2
Views
1K
MHB Find Zeros of $2x^3+5x^2-28x-15$ with Synthetic Division
  • · Replies 2 ·
Replies
2
Views
1K
Solve 2D Asteroid Problem: Step-by-Step Guide
  • · Replies 3 ·
Replies
3
Views
2K
Time period of SHM & Energy conservation in pulley-spring-block system
  • · Replies 24 ·
Replies
24
Views
4K
Resistance force changing the velocity of an object
  • · Replies 8 ·
Replies
8
Views
1K
High School Upper and Lower Bounds of Polynomials
  • · Replies 8 ·
Replies
8
Views
5K
Undergrad Different Substitution for Solving an Integral
  • · Replies 6 ·
Replies
6
Views
2K
Verify Green's Theorem in the given problem
  • · Replies 10 ·
Replies
10
Views
2K