I was at a quiz bowl competition and one of the questions was to find the roots of this polynomial. In one or two seconds after reading the question, somebody on the other team buzzed and got the right answer $(-4, -7, 11)$. How is this possible? What did he use to get the answer? This is a high school competition.
One way I suppose he could've done it is to realize that, since there is no $x^2$ term, the sum of the roots is 0, then find three integers $a, b, c$ such that $abc = 308$, but doing all of that in 1 or 2 seconds? is that possible?
Okay, so from the comments I see that it was just some really fast mental math, not some kind of advanced formula that I'm not aware of. Thanks for the help!