How do you factor #8x^3+4x^2-18x-9#?

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)