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 .

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]

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.