| Date | November 2008 | Marks available | 6 | Reference code | 08N.1.hl.TZ0.1 |
| Level | HL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
When \(f(x) = {x^4} + 3{x^3} + p{x^2} - 2x + q\) is divided by (x − 2) the remainder is 15, and (x + 3) is a factor of f(x) .
Find the values of p and q .
Markscheme
\(f(2) = 16 + 24 + 4p - 4 + q = 15\) M1
\( \Rightarrow 4p + q = - 21\) A1
\(f( - 3) = 81 - 81 + 9p + 6 + q = 0\) M1
\( \Rightarrow 9p + q = - 6\) A1
\( \Rightarrow p = 3{\text{ and }}q = - 33\) A1A1 N0
[6 marks]
Examiners report
Most candidates made a meaningful attempt at this question. Weaker candidates often made arithmetic errors and a few candidates tried using long division, which also often resulted in arithmetic errors. Overall there were many fully correct solutions.
