2026 IGCSE Additional Mathematics May/June 0606/13 Q4

2026 IGCSE Additional Mathematics May/June 0606/13 Q4

6 marks

The polynomial \(\mathrm{p}\) is given by \(\mathrm{p}(x)=4x^3-5x^2-7x+2\).

  1. Show that \(x-2\) is a factor of \(\mathrm{p}(x)\).[1]
  2. Write \(\mathrm{p}(x)\) as a product of linear factors.[3]
  3. Hence solve the equation \(4u^6-5u^4-7u^2+2=0\).[2]

Solution:

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Answer:(a) Shown. (b) \((x-2)(4x-1)(x+1)\) (c) \(u=\pm\sqrt2,\ \pm\dfrac12\)

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