
theorem :: Factor theorem (Bezout)
  for L being non degenerated comRing, r being Element of L, p, q being
  Polynomial of L st p = <%-r,1.L%>*'q holds r is_a_root_of p
proof
  let L be non degenerated comRing, r be Element of L, p, q be Polynomial of L;
  assume p = <%-r,1.L%>*'q;
  then eval(p,r) = eval(<%-r,1.L%>,r) * eval(q,r) by POLYNOM4:24
    .= (-r+r) * eval(q,r) by POLYNOM5:47
    .= 0.L * eval(q,r) by RLVECT_1:def 10
    .= 0.L;
  hence thesis;
end;
