AQA C4 2011 June — Question 1

Exam BoardAQA
ModuleC4 (Core Mathematics 4)
Year2011
SessionJune
TopicFactor & Remainder Theorem
TypeVerify factor then simplify rational expression
1 The polynomial \(\mathrm { f } ( x )\) is defined by \(\mathrm { f } ( x ) = 4 x ^ { 3 } - 13 x + 6\).
  1. Find \(\mathrm { f } ( - 2 )\).
  2. Use the Factor Theorem to show that \(2 x - 3\) is a factor of \(\mathrm { f } ( x )\).
  3. Simplify \(\frac { 2 x ^ { 2 } + x - 6 } { \mathrm { f } ( x ) }\).
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