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
