(i) Expand \((3+x)^4\), evaluating each coefficient.

In the expansion of

\(\left(x-\frac{p}{x}\right)(3+x)^4\)

the coefficient of \(x\) is zero.

(ii) Find the value of the constant \(p\).

(iii) Hence find the term independent of \(x\).

(iv) Show that the coefficient of \(x^2\) is \(90\).