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2 marksAlgebraic Operations

CAPE Pure Mathematics Unit 1 · May/June 2006 · Paper 1 · Question 1(a)(i)

The function f(x) is given by f(x) = x^4 - (p + 1)x^2 + p, where p is in N.

Show that (x - 1) is a factor of f(x) for all values of p.

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Other parts of this question

  1. 1(a)(ii)If (x - 2) is a factor of f(x), find the value of p.[2 marks]
  2. 1(b)Given that sum_(r=1)^n r = n/2(n + 1), show that sum_(r=1)^n (3r + 1) = 1/2 n(3n + 5).[4 marks]

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