2026 CCHY P1 Q8

The polynomial \(f(x)\) is such that \(f(x)=ax^3+bx^2+cx-4\), where \(a\), \(b\) and \(c\) are integers. Also, \(f'(0)=5\). It is given that \(f(x)\) has a factor of \(x-1\) and a remainder of 18 when divided by \(x+2\).

1. Find the values of \(a\), \(b\) and \(c\).[5]
2. Hence factorise \(f(x)\) completely.[2]