Edexcel P2 2021 October — Question 4

Exam BoardEdexcel
ModuleP2 (Pure Mathematics 2)
Year2021
SessionOctober
TopicFactor & Remainder Theorem
TypeProve root count with given polynomial

4. $$f ( x ) = \left( x ^ { 2 } - 2 \right) ( 2 x - 3 ) - 21$$
  1. State the value of the remainder when \(\mathrm { f } ( x )\) is divided by ( \(2 x - 3\) )
  2. Use the factor theorem to show that \(( x - 3 )\) is a factor of \(\mathrm { f } ( x )\)
  3. Hence,
    1. factorise \(\mathrm { f } ( x )\)
    2. show that the equation \(\mathrm { f } ( x ) = 0\) has only one real root.