The Waring problem for matrix algebras, II

Let f$f$ be a noncommutative polynomial of degree m > 1$m\geqslant 1$ over an algebraically closed field F$F$ of characteristic 0. If n > m-1$n\geqslant m-1$ and alpha 1,alpha 2,alpha 3$\alpha _1,\alpha _2,\alpha _3$ are nonzero elements from F$F$ such that alpha 1+alpha 2+alpha 3=0$\alpha _1+\alpha _2+\alpha _3=0$, then every trace zero nxn$n\times n$ matrix over F$F$ can be written as alpha 1A1+alpha 2A2+alpha 3A3$\alpha _1 A_1+\alpha _2A_2+\alpha _3A_3$ for some Ai$A_i$ in the image of f$f$ in Mn(F)$M_n(F)$.