Answer: Given that the following is the factor of f(x), we then have.
[tex]\begin{gathered} (x-3)y=f(x) \\ \therefore\rightarrow \\ y=\frac{f(x)}{(x-3)}=\frac{2x^3-3x^2-8x-3}{(x-3)} \end{gathered}[/tex]By algebraic long division, we then have the following.
[tex]y=2x^2+3x+1[/tex]Which can be further factorized as:
[tex]2x^2+3x+1=(2x+1)(x+1)[/tex]Therefore the complete factorization of f(x) is as follows:
[tex]f(x)=(2x+1)(x+1)((x-3)=2x^3-3x^2-8x-3[/tex]