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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.
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.
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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.
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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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
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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