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2024 CCHY P1 Q5

2024 CCHY P1 Q5

7 marks
  1. Explain why \(\frac{2x^3 - 4x^2 + 13x - 10}{(x^2 + 4)(x - 2)}\) is considered an improper fraction.[1]
  2. Express \(\frac{2x^3 - 4x^2 + 13x - 10}{(x^2 + 4)(x - 2)}\) in the form of \(A + \frac{Bx + C}{(x^2 + 4)(x - 2)}\) and hence, express \(\frac{2x^3 - 4x^2 + 13x - 10}{(x^2 + 4)(x - 2)}\) in partial fractions.[6]

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Answer:(a) The numerator and denominator both have degree \(3\), so the fraction is improper. (b) \(A=2\), \(B=5\), \(C=6\); \(2+\frac{1-2x}{x^2+4}+\frac2{x-2}\)

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