  A new recursion in only one variable allows very simple verifications of
Bressoud's polynomial identities, which lead to the Rogers-Ramanujan
identities. This approach might be compared with an earlier approach due to
Chapman. Applying the $q$-Chu-Vandermonde convolution, as suggested by Cigler,
makes the computations particularly simple and elementary. The same treatment
is also applied to the Santos polynomials and perhaps more polynomials from a
list of Rogers-Ramanujan like polynomials \cite{Sills}.
