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

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In summary, synthetic division is a faster way of doing polynomial division than normal division. It is also known as Horner's trick and is used for dividing polynomials by a linear factor. It is different from normal division in that it is a more efficient and streamlined method. However, it only works when the denominator can be factored into monomials with integer roots.
  • #1
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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  • #2
What is synthetic division and through what is it different from normal division?

Daniel.
 
  • #3
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.
 
  • #4
AAAaaaaaaaaaaaaah,i knew it under the name "Schema lui Horner" (Horner's trick).Well,wasn't that Wiki page clear??

Daniel.
 
  • #5
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.
 
  • #6
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.
 

1. What is synthetic division?

Synthetic division is a method used to divide polynomials that have a degree higher than one. It is a quicker and more efficient way of dividing than traditional long division.

2. How is synthetic division performed?

Synthetic division involves using the coefficients of the polynomial, along with the divisor, to create a simplified table. This table is then used to find the quotient and remainder of the division.

3. When should synthetic division be used?

Synthetic division is useful when dividing polynomials with a degree higher than one, and when the divisor is a linear expression (ax + b). It is also helpful when finding the roots of a polynomial.

4. What are the advantages of using synthetic division?

Synthetic division is generally faster and easier to perform than traditional long division. It also allows for easier identification of the remainder and quotient, and can be used to find the roots of a polynomial.

5. Are there any limitations to synthetic division?

Yes, synthetic division can only be used for dividing polynomials with a degree higher than one. It also only works when the divisor is a linear expression (ax + b). Additionally, it can only be used for dividing polynomials with real coefficients.

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