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Binomial Theorem and Partial Fractions

Quick questions on Partial fractions with repeated and quadratic factors explained: O-Level A-Maths

6short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is a repeated linear factor?
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A factor raised to a power, such as (x+2)2(x + 2)^2, contributes one fraction for each power up to that power:
What is an irreducible quadratic factor?
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A quadratic factor that does not factorise (its discriminant is negative), such as x2+2x^2 + 2, needs a linear numerator:
What is constant numerator over a quadratic?
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An irreducible quadratic factor needs a linear numerator Bx+CBx + C, not just a constant.
What is q1?
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State the correct partial-fraction form for 1(x+3)(x2+1)\dfrac{1}{(x + 3)(x^2 + 1)}. [1 mark]
What is q2?
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State the form for x(x−2)2(x+1)\dfrac{x}{(x - 2)^2(x + 1)}. [2 marks]
What is q3?
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Express 4(x−1)2\dfrac{4}{(x - 1)^2} in partial fractions. [2 marks]

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