0606/23 Oct/Nov 2025, Question 1: The Factor and Remainder Theorems
Cambridge IGCSE Additional Mathematics 0606 · Paper 23 (Calculator) · Calculator · 5 marks
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The question, in short
Given p(x) = ax³ − 7x² − bx + 9 with x − 3 a factor and remainder −35 when divided by x + 2, find the constants a and b.
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Solution · 5 marks
- 1p(3) = 0: 27a − 63 − 3b + 9 = 0, so 9a − b = 18
- 2p(−2) = −35: −8a − 28 + 2b + 9 = −35, so −8a + 2b = −16, i.e. 4a − b = 8
- 3Subtracting: 5a = 10, so a = 2
- 4b = 9(2) − 18 = 0
Answera = 2, b = 0
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Also searched as: 0606/23/O/N/25 · 0606_w25_qp_23 · 0606 w25 23 · question 1.
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