Repeated linear factor with distinct linear factor – decompose only

Denominator contains one repeated linear factor and one or more distinct linear factors; express in partial fractions only, with no integration required.

3 questions · Moderate -0.1

1.02y Partial fractions: decompose rational functions
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OCR C4 2010 June Q3
5 marks Moderate -0.3
3 Express \(\frac { x ^ { 2 } } { ( x - 1 ) ^ { 2 } ( x - 2 ) }\) in partial fractions.
OCR C4 2013 June Q1
5 marks Standard +0.3
1 Express \(\frac { ( x - 7 ) ( x - 2 ) } { ( x + 2 ) ( x - 1 ) ^ { 2 } }\) in partial fractions.
AQA Paper 1 2020 June Q9
7 marks Moderate -0.3
9
    1. By using a counter example, show that the answer obtained by Chloe cannot be correct.
      9
      1. (ii) Explain her mistake in Step 1.
        9
    2. Write \(\frac { 2 x ^ { 2 } + x } { ( x + 1 ) ( x + 2 ) ^ { 2 } }\) as partial fractions, with constant numerators.