2025 SCGS PRELIMS P1 Q6
2025 SCGS PRELIMS P1 Q6
Secondary 4
7 marks
- By using long division, show that \(2x^2+1\) is a factor of \(2x^3-4x^2+x-2\).[2]
- Express \(\dfrac{11x-5x^2-11}{2x^3-4x^2+x-2}\) in partial fractions.[5]
Solution:
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Answer:(a) \(2x^3-4x^2+x-2=(2x^2+1)(x-2)\), so \(2x^2+1\) is a factor. (b) \(\dfrac{11x-5x^2-11}{2x^3-4x^2+x-2}=-\dfrac{1}{x-2}+\dfrac{5-3x}{2x^2+1}\).
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