2023 SJI P2 Q4

In the binomial expansion of \((1+px)^n\), where \(p,n\in\mathbb Z\), the coefficient of \(x\) is \(-4\) and the coefficient of \(x^2\) is \(12\).

1. Show that \(p=2\) and find the value of \(n\).[4]
2. Find the coefficient of \(x^3\).[1]
3. State the range of values of \(x\) for which the binomial expansion is valid.[1]