Question

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

Answer 1

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)