2025 AISS PRELIMS P2 Q2

2025 AISS PRELIMS P2 Q2

Secondary 4
7 marks
2025 Ahmad Ibrahim Secondary School Prelims A Math Paper 2
  1. Factorise \(x^3+27k^3\) as a product of a linear and a quadratic factor.[2]
  2. Hence solve \(x^3+27=(x+3)(x+10)\), expressing non-integer roots in surd form.[3]
  3. Find the value of \(k\) given that \(x^3+27k^3\) leaves a remainder of 351 when divided by \(x-2\).[2]

Solution:

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Answer:(a) \((x+3k)(x^2-3kx+9k^2)\) (b) \(x=-3,\ 2\pm\sqrt5\) (c) \(k=\dfrac73\)

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