Representations of polynomials over finite fields of characteristic two as A2+A+BC+D3A2+A+BC+D3

Let FqFq be a finite field of characteristic 2, with q   elements. If q⩾8q⩾8 then every polynomial P∈Fq[t]P∈Fq[t] has a strict representation P=A2+A+BCP=A2+A+BC, i.e.:max(deg(A2),deg(B2),deg(C2))