We are asked to sum the two trinomials [tex](-4f^3-5f+16)+(4f^2-f+9)[/tex]. We can start by using the distributive property to remove the parenthesis, giving us [tex]-4f^3-5f+16+4f^2-f+9[/tex]. Next, when we combine like terms, we get [tex]\boxed{-4f^3+4f^2-6f+25}[/tex]. Hope this helped!