Synthetic division or Long division of polynomials?

  • Thread starter streetmeat
  • Start date
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

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

HallsofIvy

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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

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Synthetic division only works if you are dividing a polynomial by a linear factor..
There is a generalization to arbitrary polynomials
 

lurflurf

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http://www.pims.math.ca/pi/issue7/page13-16.pdf [Broken]
 
Last edited by a moderator:
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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