Synthetic division or Long division of polynomials?

1. Jul 20, 2007

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?

2. Jul 20, 2007

Gib Z

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

3. Jul 20, 2007

derekjn

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

4. Jul 20, 2007

HallsofIvy

Staff Emeritus
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.

5. Jul 24, 2007

lurflurf

There is a generalization to arbitrary polynomials

6. Jul 24, 2007

lurflurf

7. Jun 18, 2008

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);

:)