All the potential zeros are ± all fractions whose numerators are divisors of the constant term, 12, and whose denominators are divisors of the leading coefficient 8. The divisors of constant term 12 are (1,2,3,4,6,12} The divisors of leading coefficient 8 are {1,2,4,8} The only potential zeros are and after reducing, we have: And after eliminating the duplications, the list shortens to: We see that the graph only crosses the x axis between -2 and -3, and -3 is not a zero. None of the others are between -2 and -3, so it has no rational zeros, only the irrational one between -2 and -3. That means that the polynomial cannot be factored, and is therefore prime. Edwin