In the paper a result in connection with the distortion of the cross ratio of four points under the mapping defined by a complex polynomial with restricted critical values is proved. The corollaries deduced from this result include some inequalities which involve the absolute value and certain coefficients of a polynomial. In particular, the author obtains an exact lower bound for the maximum moduli of the critical values of a polynomial \(P\) of degree \(n\) which is normalized by the following conditions: i) the value of \(P\) at the origin is zero and ii) its derivative at the origin is non-zero.