2026 IGCSE Additional Mathematics May/June 0606/12 Q3

2026 IGCSE Additional Mathematics May/June 0606/12 Q3

7 marks

The polynomial \(\mathrm{p}\) is given by \(\mathrm{p}(x)=6x^3-x^2-5x+2\).

  1. Find the remainder when \(\mathrm{p}(x)\) is divided by \(x+2\).[1]
  2. Write \(\mathrm{p}(x)\) as a product of linear factors.[4]
  3. Hence solve the equation \(6u^6-u^4-5u^2+2=0\).[2]

Solution:

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Answer:(a) \(-40\) (b) \((x+1)(3x-2)(2x-1)\) (c) \(u=\pm\sqrt{\dfrac23},\ \pm\dfrac1{\sqrt2}\)

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