



 
There is a "cubic formula" (in fact two versions, a radical version and one using trig functions) and a "quartic formula" but they are usually more trouble than less powerful methods. If there are repeating patterns in a polynomial they may indicate a factorization in the same way that (say) 424242 = 10101 * 42. Once you find one factor, divide it out and the quotient will be lowerorder. IF the coefficients of the factors are as (Ax+a)(Bx+b)(Cx+c) [ABc+AbC+aBC]x^{2} and the linear term [abC+aBc+Abc]x to see which combination works. That should get the second one (not without some effort!) Finally, a quartic with no odd (x or x^{3}) terms can often be solved by setting y=x^{2} to get a quadratic in y. The roots of this may be of the form Ax^{2} + a and irreducible; or they may be of the form Ax^{2}  a and factor further. This will work for your example. Over the reals not every quadratic factors; you can use other tricks such as x^{4} + x^{2} + 1 = (x^{4} + 2x^{2} +1)  x^{2} Good Hunting!  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 