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Methods in Algebra and Calculus

Quick questions on Partial fractions: linear, repeated and quadratic factors - SQA Advanced Higher Maths

4short 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 only one term for a repeated factor?
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A factor (xβˆ’a)2(x - a)^2 needs both Axβˆ’a\dfrac{A}{x - a} and B(xβˆ’a)2\dfrac{B}{(x - a)^2}; one term alone cannot reproduce the original fraction.
What is a constant over a quadratic?
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Over an irreducible quadratic the numerator is linear, Bx+CBx + C, not a single constant.
What is q1?
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Express 7(xβˆ’3)(x+4)\dfrac{7}{(x - 3)(x + 4)} in partial fractions. [3 marks]
What is q2?
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Write x(xβˆ’2)2\dfrac{x}{(x - 2)^2} in partial fractions. [3 marks]

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