Edexcel C2 — Question 13

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
TopicFactor & Remainder Theorem
TypeSingle unknown from factor condition

13. \(\mathrm { f } ( x ) = x ^ { 3 } - x ^ { 2 } - 7 x + c\), where \(c\) is a constant. Given that \(\mathrm { f } ( 4 ) = 0\),
  1. find the value of \(c\),
  2. factorise \(\mathrm { f } ( x )\) as the product of a linear factor and a quadratic factor.
  3. Hence show that, apart from \(x = 4\), there are no real values of \(x\) for which \(\mathrm { f } ( x ) = 0\).