Consider the following statements relating to the level of poker play of four players $$P, Q, R$$ and $$S.$$

$$\,\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,\,$$ P always beats Q
$$\,\,\,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,\,\,\,\,$$ R always beats S
$$\,\,\,\,\,{\rm I}{\rm I}{\rm I}.\,\,\,\,\,\,\,\,$$ S loses to P only sometimes
$$\,\,\,\,\,{\rm I}V.\,\,\,\,\,\,\,\,$$ R always loses to Q

Which of the following can be logically inferred from the above statements?

$$\,\,\,\,\,\,\,\,\,\left( i \right)\,\,\,\,\,\,\,\,$$ P is likely to beat all the three other players
$$\,\,\,\,\,\,\,\,\left( ii \right)\,\,\,\,\,\,\,$$ S is the absolute worst player in the set

If $$f\left( x \right) = 2{x^7} + 3x - 5,$$ which of the following is a factor of $$f(x)$$?