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

Quote by derekjn

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);

:)

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streetmeat	Synthetic division or Long division of polynomials? Tweet 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 Recognitions: Homework Help	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 Recognitions: Gold Member Science Advisor Staff Emeritus	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 Recognitions: Homework Help	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); :)