| Date | May 2010 | Marks available | 5 | Reference code | 10M.1.hl.TZ1.1 |
| Level | HL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
Given that \(A{x^3} + B{x^2} + x + 6\) is exactly divisible by \((x +1)(x − 2)\), find the value of A and the value of B .
Markscheme
using the factor theorem or long division (M1)
\( - A + B - 1 + 6 = 0 \Rightarrow A - B = 5\) (A1)
\(8A + 4B + 2 + 6 = 0 \Rightarrow 2A + B = - 2\) (A1)
\(3A = 3 \Rightarrow A = 1\) (A1)
\(B = - 4\) (A1) (N3)
Note: Award M1A0A0A1A1 for using \((x - 3)\) as the third factor, without justification that the leading coefficient is 1.
[5 marks]
Examiners report
Most candidates attempted this question and it was the best done question on the paper with many fully correct answers. It was good to see a range of approaches used (mainly factor theorem or long division). A number of candidates assumed \((x - 3)\) was the missing factor without justification.
