NumericalModerate3 marks
If (x + 2) and (x + 3) are factors of x³ + ax + b, find the values of 'a' and 'b'.
Topic: Remainder and factor theorem
Previous-year question practice database
Answer
Solution diagram
Exam answer
b = –30
Explanation
(x + 2) and (x + 3) factors → x3
+ ax + b f (–2) = (–2)3 + a (–2) + b f(–3) = (–3)3 + a(–3) + b ∴0 = –8 – 2a + b ⇒ –2a + b = 8 0 = –27 – 3a + b⇒ –3a + b = 27 –2a + b = 8 –3a + b = 27 + – – a = –19 38 + b = 8 b = –30
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