Synthetic division or Long division of polynomials?

[streetmeat]

How do i know under which circumstances to use synthetic and when to just do regular polynomial division? do they not both give the same results?

 

[Gib Z]

Yes, they give the same results. They are just 2 different methods for the same thing, I prefer the long division though.

 

[derekjn]

Synthetic division only works if you are dividing a polynomial by a linear factor..

 

[HallsofIvy]

In fact, only when dividing by something of the form x-a.

Synthetic division is just a simplified way of writing a division of that very special (but very important) form.

 

[lurflurf]

Synthetic division only works if you are dividing a polynomial by a linear factor..

There is a generalization to arbitrary polynomials

 

[lurflurf]

http://www.pims.math.ca/pi/issue7/page13-16.pdf

 

[jerckomilicic]

Hi i find them to go together, hand in hand.

for instance, we have this problem: 8x^6 + 7x^3 -1

i use synthetic division to find that -1 is a solution, hence i have a factor that is:
(x-1)

now, to look for the rest of the factors, i use long division to divide (8x^6 + 7x^3 -1)
by (x-1);


:)