AQA C1 2015 June — Question 7 3 marks

Exam BoardAQA
ModuleC1 (Core Mathematics 1)
Year2015
SessionJune
Marks3
TopicFactor & Remainder Theorem
TypeDirect remainder then factorise
7
  1. Sketch the curve with equation \(y = x ^ { 2 } ( x - 3 )\).
  2. The polynomial \(\mathrm { p } ( x )\) is given by \(\mathrm { p } ( x ) = x ^ { 2 } ( x - 3 ) + 20\).
    1. Find the remainder when \(\mathrm { p } ( x )\) is divided by \(x - 4\).
    2. Use the Factor Theorem to show that \(x + 2\) is a factor of \(\mathrm { p } ( x )\).
    3. Express \(\mathrm { p } ( x )\) in the form \(( x + 2 ) \left( x ^ { 2 } + b x + c \right)\), where \(b\) and \(c\) are integers.
    4. Hence show that the equation \(\mathrm { p } ( x ) = 0\) has exactly one real root and state its value.
      [0pt] [3 marks]
This paper (8 questions)
View full paper
Q1 Q2 5 Q3 5 Q4 Q5 Q6 4 Q7 3 Q8