Question

f(x)=x^3+6x^2-9x-54 ... find only the rational zeros.

Answer 1

all of the zeroes are rational. I checked a couple integers until one worked. x=3 is a root. So we can factor out (x-3). Using division we get (x-3)(x^2+9x+18). This factors nicely as (x-3)(x+3)(x+6). The zeroes are 3,-3,-6, which are all rational.