I've encountered the problem:

x^3 - 10x - 12

I am suppose to;

a.) list all possible rational roots

b.) use synthetic division to test

c.) find an actual root and use the quotient I found in part "b" to find the remaining roots and solve

So here's what happened:

1. I found all of the possible rational zeros

2. I used synthetic division on each possible root, none of which equaled zero.

3. For part "b" I assumed that there is no zero for this problem...

4. I check the answer in the back of my textbook and found the answer to "b" :

b.) -2

and c.) {-2, 1 + √7, 1 - √7}

I've done all I possibly can with what I know and I couldn't come up with the same answer in the textbook..