Question

Factor completely. If a polynomial is prime, state this.

-9+18x²+21x

Answer 1

Great question.  I'd start by reorganizing the expression in descending order.  so 18x^2+21x-9. 
then, factor out any common factor: 3(6x^2+7x-3)
Then, factor into two binomials.  3(2x+3)(3x-1).  And you're done.

Answer 2

first order in decending order of powers
18x^2+21x-9
now factor out 3 we can see
(3)(6x^2+7x-3)
trial and error
(3)(2x+3)(3x-1)