I have an equation $f(x)=x^4+4x^3+2x^22-x+6$. In the past I was taught to factor it by getting the zeros by getting $p/q$, and start guessing zeros, and plugging them into the function. Once I got one or two, I would try to divide the function by them to get the rest.
It would seem to me that there has to be a much easier way of doing this. Some kind of trick. If the equation was only something like $f(x)=x^2+5x-6$, then it would be easy. just find the number that multiplies together to equal $-6$, and adds up to equal $5$. The answer would be $(x+6)(x-1)$. Is there some trick like this for functions with a degree higher than $2$?