0606/21 Oct/Nov 2025, Question 1: The Factor and Remainder Theorems
Cambridge IGCSE Additional Mathematics 0606 · Paper 21 (Calculator) · Calculator · 5 marks
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The question, in short
Given p(x) = x³ + ax² + bx − 2 with x + 2 a factor and remainder 40 when divided by x − 3, find the constants a and b.
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Solution · 5 marks
- 1p(−2) = 0: −8 + 4a − 2b − 2 = 0, so 2a − b = 5
- 2p(3) = 40: 27 + 9a + 3b − 2 = 40, so 3a + b = 5
- 3Adding: 5a = 10, so a = 2
- 4b = 2a − 5 = −1
Answera = 2 and b = −1
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Also searched as: 0606/21/O/N/25 · 0606_w25_qp_21 · 0606 w25 21 · question 1.
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