polynomial constructs a polynomial from its coefficients,
  i.e., p[1:k] specifies the polynomial
  $$p_1 + p_2 x + p_3 x^2 + \dots + p_k x^{k-1}.$$
  Internally, polynomials are simply numeric coefficient vectors of
  class "polynomial".  Several useful methods are available for
  this class, such as coercion to character (as.character()) and
  function (as.function.polynomial), extraction of
  the coefficients (coef()), printing (using as.character),
  plotting (plot.polynomial), and computing sums and
  products of arbitrarily many polynomials.
as.polynomial tries to coerce its arguments to a polynomial.
is.polynomial tests whether its argument is a polynomial (in
  the sense that it has class "polynomial".