OCR C2 — Question 6

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
TopicFactor & Remainder Theorem
TypeFind constant, factorise completely

6. Given that $$f ( x ) = x ^ { 3 } + 7 x ^ { 2 } + p x - 6$$ and that \(x = - 3\) is a solution to the equation \(\mathrm { f } ( x ) = 0\),
  1. find the value of the constant \(p\),
  2. show that when \(\mathrm { f } ( x )\) is divided by \(( x - 2 )\) there is a remainder of 50 ,
  3. find the other solutions to the equation \(\mathrm { f } ( x ) = 0\), giving your answers to 2 decimal places.