2026 CVSS P2 Q4

Do not use a calculator in this question.

A polynomial is given by \(f(x)=4x^3-2px^2+p(p-4)x-8\), where \(p\) is a constant.

1. Find the remainder when \(f(x)\) is divided by \(x\).[2]
2. Given that \(x-p\) is a factor of \(f(x)\), show that \(3p^3-4p^2-8=0\).[2]
3. Find the value(s) of \(p\).[5]