2026 CSS P1 Q11

2026 CSS P1 Q11

Secondary 4
10 marks
  1. Show that \(x-1\) is a factor of \(f(x)=x^3+x^2-x-1\). Hence or otherwise, factorise \(f(x)\). Show your working clearly.[3]
  2. Express \(\dfrac4{x^3+x^2-x-1}\) as a sum of 3 partial fractions.[7]

Solution:

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Answer:(a) \((x-1)(x+1)^2\). (b) \(\dfrac1{x-1}-\dfrac1{x+1}-\dfrac2{(x+1)^2}\).

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