To factor the expression 15x^3 + 29x^2 - 8x - 12, we can first look for any common factors among the terms. In this case, there are no common factors among all four terms.

Next, we can try to factor by grouping. We group the terms in pairs:

(15x^3 + 29x^2) + (-8x - 12)

Now, we can factor out the greatest common factor from each pair separately:

x^2(15x + 29) - 4(2x + 3)

Now, we can see that we have a common binomial factor of (15x + 29) in both terms. We can factor it out:

(15x + 29)(x^2 - 4)

The expression 15x^3 + 29x^2 - 8x - 12 can be factored as (15x + 29)(x^2 - 4).