Question

Here is something I have not seen up here yet.

\[f(x) * g(x) = 2x^2 +9x - 5 \]

Answer 1

Factor the polynomial and one factor is f and the other is g\[f*g=(x-1)(2x+5)\]==>\[f(x)=x-1;g(x)=2x+5\]or vice versa

Answer 2

of course you could use any f and g right? put
\[f(x)=\text{whatever}\] and
\[g(x)=\frac{2x^2+9x-5}{\text{whatever}}\]

Answer 3

Yes the answer is not unique