Respuesta :

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]

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