
theorem Th46:
  for L being non trivial comRing, x being Element of L, p, q
  being Polynomial of L st p = <%-x,1.L%>*'q holds x is_a_root_of p
proof
  let L be non trivial comRing, x be Element of L, p, q be Polynomial of L
  such that
A1: p = <%-x,1.L%>*'q;
A2: eval(<%-x,1.L%>,x) = (-x)+x by POLYNOM5:47
    .= 0.L by RLVECT_1:5;
  thus eval(p,x) = eval(<%-x,1.L%>,x) * eval(q,x) by A1,POLYNOM4:24
    .= 0.L by A2;
end;
