This expression is a good candidate for "factoring by grouping." I note that the first 2 terms and the last 2 terms share a common factor, 2x+1:
8x^3 + 4x^2 - 18x - 9
4x^2 *(2x + 1) -9 (2x+1)
This can be re-written as (2x+1)(4x2-9)
The latter factor is also easily factorable:
(2x+1)(2x-3)(2x+3) (answer)
