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6 marksAlgebraic Operations

CAPE Pure Mathematics Unit 1 · May/June 2016 · Paper 2 · Question 1(a)(ii)

A function f(x) is defined as 2x³ - x² + px + q. It is given that (x + 3) is a factor of f(x) and that f(x) has a remainder of 10 when divided by (x + 1).

Hence, solve the equation f(x) = 0.

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Other parts of this question

  1. 1(a)(i)Show that p = -25 and q = -12.[7 marks]
  2. 1(b)Use mathematical induction to prove that 6ⁿ - 1 is divisible by 5 for all natural numbers n.[6 marks]
  3. 1(c)(i)Complete the truth table below:[4 marks]
  4. 1(c)(ii)State, giving a reason for your response, whether the following statements are logically equivalent: p → q and ¬(p ∨ q) → (p ∧ q).[2 marks]

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