What is (f*g)What is (f⋅g)(x)?

\((f\cdot g)(x)=f(x)\cdot g(x)\)

 

I attest that the notation is funky. It should be relatively simple from here.

 

\(f(x)=x^3-4x+2\\ g(x)=x^2+2\)	Just multiply them together.
\((f\cdot g)(x)=(x^3-4x+2)(x^2+2)\)	Now, you are on a mission to find the product of the trinomial and binomial.
\((f\cdot g)(x)=x^5\textcolor{red}{-4x^3}+2x^2\textcolor{red}{+2x^3}-8x+4\)	Now, combine any existing like terms, which I highlighted for you in red.
\((f\cdot g)(x)=x^5-2x^3+2x^2-8x+4\)