Hi;

I know how to dertermine if quadratics factor

But how do you dertermine if higher order polynomials factor?

Is it just trial and error and remainder theorem?

Thanks.

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- Aug 3rd 2012, 12:11 AManthonyefactor higher order polynomials
Hi;

I know how to dertermine if quadratics factor

But how do you dertermine if higher order polynomials factor?

Is it just trial and error and remainder theorem?

Thanks. - Aug 3rd 2012, 01:03 AMProve ItRe: factor higher order polynomials
All cubic and quartic equations can be solved. Any higher polynomial can not.

http://homepage.smc.edu/kennedy_john/SOLVINGCUBICS.PDF

http://homepage.smc.edu/kennedy_john...CEQUATIONS.PDF - Aug 3rd 2012, 04:55 AMHallsofIvyRe: factor higher order polynomials
Well, let's call it

**educated**trial and error! To determine whether or not a polynomial has a factor with integer coefficients we can use the "rational root theore": If $\displaystyle \frac{p}{q}$ satisfies the polynomial equation $\displaystyle a_nx^n+ a_{n-1}x^{n-1}+\cdot\cdot\cdot+ a_1x+ a_0= 0$ then the numerator, p, evenly divides the "constant term", $\displaystyle a_0$, and the denominator, m, evenly divides the "leading coefficient", $\displaystyle a_n$. That allows you to reduce to a finite number of trials. However,**Most**polynomials do NOT factor with integer or rational number coefficients. There is no good "trial and error" method to find non-rational factors or non-rational roots except to use "completing the square" for quadratics and the general formulas for quadratic, cubic, and quartic polynomials. There are no formulas for higher degree equations**in terms or radicals**because some higher degree equations have roots that cannot be written in terms of radicals.