| Date | None Specimen | Marks available | 6 | Reference code | SPNone.2.hl.TZ0.1 |
| Level | HL only | Paper | 2 | Time zone | TZ0 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
Given that (x − 2) is a factor of \(f(x) = {x^3} + a{x^2} + bx - 4\) and that division \(f(x)\) by (x − 1) leaves a remainder of −6 , find the value of a and the value of b .
Markscheme
\(f(2) = 8 + 4a + 2b - 4 = 0\) M1
\( \Rightarrow 4a + 2b = - 4\) A1
\(f(1) = 1 + a + b - 4 = - 6\) M1
\( \Rightarrow a + b = - 3\) A1
solving, \(a = 1,{\text{ }}b = - 4\) A1A1
[6 marks]
Examiners report
[N/A]
