What are the rational zeros for #x^3-3x^2-4x+12#?
To solve this problem we can use the p/q method where p is the constant and q is the leading coefficient.
This gives us +-12/1 which gives us potential factors +-1, +-2, +-3, +-4, +-6, and +-12.
Now we have to use synthetic division to divide the cubic function. It's easier to start with the +-1 and then the +-2 and so on. When using synthetic division, we must have a remainder of 0 for the dividend to be a zero.
Using synthetic division to get our equation to a quadratic, then by factoring the quadratic, we find the roots are 2, -2, and 3.