Edexcel C2 — Question 9

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
TopicFactor & Remainder Theorem
TypeVerify factor then sketch or analyse curve

9. \(f ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 3 x + 18\).
  1. Show that \(( x - 3 )\) is a factor of \(\mathrm { f } ( x )\).
  2. Fully factorise \(\mathrm { f } ( x )\).
  3. Using your answer to part (b), write down the coordinates of one of the turning points of the curve \(y = \mathrm { f } ( x )\) and give a reason for your answer.
  4. Using differentiation, find the \(x\)-coordinate of the other turning point of the curve \(y = \mathrm { f } ( x )\).