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4 marksAlgebraic Operations

CAPE Pure Mathematics Unit 1 · May/June 2017 · Paper 2 · Question 1(c)(i)

The polynomial f(x) = ax³ + 9x² – 11x + b has a factor of (x - 2) and a remainder of 12 when divided by (x + 2).

Show that a = 2 and b = -30.

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Other parts of this question

  1. 1(a)(i)Write EACH of the statements below in terms of p and q. It is not raining or John is sick.[1 mark]
  2. 1(a)(ii)Write EACH of the statements below in terms of p and q. If it is raining then John is not sick.[1 mark]
  3. 1(b)(i)Prove that * is commutative.[1 mark]
  4. 1(b)(ii)Show that the identity element of * is 3.[2 marks]
  5. 1(c)(ii)Hence, solve ax³ + 9x² – 11x + b = 0.[9 marks]
  6. 1(d)Use mathematical induction to prove that 8+16+24+ 32 + ... + 8n = 4n(n + 1) for all n ∈ N.[7 marks]

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