reserve n for Nat;

theorem cc4:
for F being algebraic-closed Field,
    p being non constant Polynomial of F
ex a being Element of F, q being Ppoly of F,(BRoots p) st a * q = p
proof
let F be algebraic-closed Field, p be non constant Polynomial of F;
consider q being (Ppoly of F,BRoots p),
         r being non with_roots Polynomial of F such that
A: p = q *' r & Roots q = Roots p by acf;
reconsider r1 = r as Element of the carrier of Polynom-Ring F
   by POLYNOM3:def 10;
len r - 1 <= 1 - 1 by XREAL_1:9,POLYNOM5:def 9;
then r1 is constant by HURWITZ:def 2;
then consider a being Element of F such that B: r1 = a|F by RING_4:20;
take a,q;
thus p = q *' (a * 1_.(F)) by A,B,RING_4:16
      .= a * (q *' 1_.(F)) by RATFUNC1:6
      .= a * q;
end;
