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Synthetic division or Long division of polynomials?

by streetmeat
Tags: division, polynomials, synthetic
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streetmeat
#1
Jul20-07, 12:13 AM
P: 8
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?
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Gib Z
#2
Jul20-07, 01:31 AM
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Yes, they give the same results. They are just 2 different methods for the same thing, I prefer the long division though.
derekjn
#3
Jul20-07, 03:17 AM
P: 12
Synthetic division only works if you are dividing a polynomial by a linear factor..

HallsofIvy
#4
Jul20-07, 05:54 AM
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P: 39,568
Synthetic division or Long division of polynomials?

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
#5
Jul24-07, 03:24 PM
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Quote Quote by derekjn View Post
Synthetic division only works if you are dividing a polynomial by a linear factor..
There is a generalization to arbitrary polynomials
lurflurf
#6
Jul24-07, 03:42 PM
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http://www.pims.math.ca/pi/issue7/page13-16.pdf
jerckomilicic
#7
Jun18-08, 07:19 AM
P: 1
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);


:)


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