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#1 2006-11-15 19:49:15

wildmood
Guest

4 degree polynomials

Hi,

is there a formula to factorize quadric polynomials.

i need a formula how to factorize x^4-3x^3+3x+1.

i can factorize it (x^2-x-1)(x^2-2x-1) however need to know if there is any general formula for this kind of polynomials.

#2 2006-11-16 00:54:36

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: 4 degree polynomials

I'm pretty sure that there isn't a formula for quartic equations.

You'd need to look for values of x that make the function equal 0, and then you'd know that a factor of the function is (x-a), where a was your x-value.

Then you could use polynomial division and then you'd be left with a cubic, which you could do the same thing on.

That doesn't work with yours though, so the best way is probably just to get a calculator to do it for you. smile


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#3 2006-11-16 01:05:38

wildmood
Guest

Re: 4 degree polynomials

I thought I've seen the forumal somewhere - quartic with -3 and 3 as the second and third coefficients, but maybe I'm wrong. I managed to factorize it myself by trial and error - in this case it wasn't too difficult.

#4 2006-11-16 03:25:19

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: 4 degree polynomials

there IS a formula to solve the general quartic, however, its extremely unstable and long winded.

when i say formula, i mean a long list of steps to take, involving complex numbers, even though the coeffecients may be real.

Last edited by luca-deltodesco (2006-11-16 03:25:55)


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#5 2006-11-16 07:20:11

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: 4 degree polynomials

There is a general formula and it is very usable... by computer programs.  Otherwise, I would be tempted to say it is merely and item of fascination and not something actually useful, as luca said.

http://en.wikipedia.org/wiki/Quartic_formula


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