Question 142964
Any rational zero can be found through this equation


*[Tex \LARGE Roots=\frac{p}{q}] where p and q are the factors of the last and first coefficients



So let's list the factors of -2 (the last coefficient):


*[Tex \LARGE p=\pm1, \pm2]


Now let's list the factors of 3 (the first coefficient):


*[Tex \LARGE q=\pm1, \pm3]


Now let's divide each factor of the last coefficient by each factor of the first coefficient



*[Tex \LARGE \frac{1}{1}, \frac{1}{3}, \frac{2}{1}, \frac{2}{3}, -\frac{1}{1}, -\frac{1}{3}, -\frac{2}{1}, -\frac{2}{3}]







Now simplify. These are all the distinct rational zeros of the function that could occur


*[Tex \LARGE  1, \frac{1}{3}, 2, \frac{2}{3}, -1, -\frac{1}{3}, -2, -\frac{2}{3}]