  The ratio monotonicity of a polynomial is a stronger property than
log-concavity. Let P(x) be a polynomial with nonnegative and nondecreasing
coefficients. We prove the ratio monotone property of P(x+1), which leads to
the log-concavity of P(x+c) for any $c\geq 1$ due to Llamas and
Mart\'{\i}nez-Bernal. As a consequence, we obtain the ratio monotonicity of the
Boros-Moll polynomials obtained by Chen and Xia without resorting to the
recurrence relations of the coefficients.
