AQA C4 2006 June — Question 1

Exam BoardAQA
ModuleC4 (Core Mathematics 4)
Year2006
SessionJune
TopicPolynomial Division & Manipulation
1
  1. The polynomial \(\mathrm { p } ( x )\) is defined by \(\mathrm { p } ( x ) = 6 x ^ { 3 } - 19 x ^ { 2 } + 9 x + 10\).
    1. Find \(\mathrm { p } ( 2 )\).
    2. Use the Factor Theorem to show that ( \(2 x + 1\) ) is a factor of \(\mathrm { p } ( x )\).
    3. Write \(\mathrm { p } ( x )\) as the product of three linear factors.
  2. Hence simplify \(\frac { 3 x ^ { 2 } - 6 x } { 6 x ^ { 3 } - 19 x ^ { 2 } + 9 x + 10 }\).
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