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0580/23 Oct/Nov 2022, Question 22: Algebraic Fractions

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Calculator · 7 marks

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The question, in short

Multiply out and collect terms for the product of three linear brackets, then combine a division of algebraic fractions into one simplified fraction.

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Part (a) · 3 marks

Multiply out (2x − 1)(x + 4)(x − 3) and collect like terms to give the expanded polynomial.

  1. 1(2x − 1)(x + 4) = 2x² + 7x − 4
  2. 2(2x² + 7x − 4)(x − 3) = 2x³ − 6x² + 7x² − 21x − 4x + 12
  3. 3= 2x³ + x² − 25x + 12

Answer2x³ + x² − 25x + 12

Part (b) · 4 marks

Divide 4/(2x − 3) by (2x² + 14x)/(2x² + 11x − 21) and give the result as one fraction in simplest form.

  1. 1= 4/(2x − 3) × (2x² + 11x − 21)/(2x² + 14x)
  2. 22x² + 11x − 21 = (2x − 3)(x + 7)
  3. 32x² + 14x = 2x(x + 7)
  4. 4= 4(2x − 3)(x + 7) / ((2x − 3) × 2x(x + 7))
  5. 5= 4/(2x) = 2/x

Answer2/x

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Also searched as: 0580/23/O/N/22 · 0580_w22_qp_23 · 0580 w22 23 · question 22.
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