Edexcel C1 2006 June — Question 9

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Year2006
SessionJune
TopicCurve Sketching
TypeFactorise then sketch

9. Given that \(\mathrm { f } ( x ) = \left( x ^ { 2 } - 6 x \right) ( x - 2 ) + 3 x\),
  1. express \(\mathrm { f } ( x )\) in the form \(x \left( a x ^ { 2 } + b x + c \right)\), where \(a\), \(b\) and \(c\) are constants.
  2. Hence factorise \(\mathrm { f } ( x )\) completely.
  3. Sketch the graph of \(y = \mathrm { f } ( x )\), showing the coordinates of each point at which the graph meets the axes.