To determine the given function using a remainder theorem :
[tex]f(x)=x^4+5x^3+5x^2-5x-6[/tex]
The given function can be solved by substituting x = 3
[tex]\begin{gathered} f(x)=x^4+5x^3+5x^2-5x-6 \\ f(3)=3^4+5(3)^3+5(3)^2-5(3)-6 \\ f(3)=81+135+45-15-6 \end{gathered}[/tex]
Adding up the values
[tex]\begin{gathered} f(3)=81+135+45-15-6 \\ f(3)=240 \end{gathered}[/tex]
Hence the final value of f(3) = 240
