Question 1 - A-Level Maths

Given that \(p = \log _ { q } 16\), express in terms of \(p\),
1. \(\log _ { q } 2\),
2. \(\log _ { q } ( 8 q )\).
  [0pt] [P2 January 2002 Question 2]
3. \(\mathrm { f } ( x ) = x ^ { 3 } - x ^ { 2 } - 7 x + c\), where \(c\) is a constant.
Given that \(\mathrm { f } ( 4 ) = 0\),
find the value of \(c\),
factorise \(\mathrm { f } ( x )\) as the product of a linear factor and a quadratic factor.
Hence show that, apart from \(x = 4\), there are no real values of \(x\) for which \(\mathrm { f } ( x ) = 0\).