0606/13 May/Jun 2025, Question 3: Dividing Polynomials
Cambridge IGCSE Additional Mathematics 0606 · Paper 13 (Non-calculator) · Non-calculator · 5 marks
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The question, in short
A cubic x³ + Ax + 30 leaves remainder 84 on division by x + 2. Determine A, then express the cubic as a product of linear factors.
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Solution · 5 marks
- 1p(−2) = −8 − 2A + 30 = 84
- 222 − 2A = 84, so A = −31
- 3p(x) = x³ − 31x + 30; p(1) = 1 − 31 + 30 = 0, so (x − 1) is a factor
- 4p(x) = (x − 1)(x² + x − 30)
- 5= (x − 1)(x − 5)(x + 6)
Answerp(x) = (x − 1)(x − 5)(x + 6)
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Also searched as: 0606/13/M/J/25 · 0606_s25_qp_13 · 0606 s25 13 · question 3.
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