Algebra and functions

Sample questions

Original practice questions written in the style of the exam.

1. Question 16 marks

   $f(x) = 2x^3 + ax^2 + bx - 6$, where $a$ and $b$ are constants.

   Given that $(x - 2)$ is a factor of $f(x)$, and that the remainder when $f(x)$ is divided by $(x + 1)$ is 6,

   (a) find the values of $a$ and $b$,

   (b) hence factorise $f(x)$ completely.

   Mark scheme

   • M1 Sets $f(2) = 0$: $16 + 4a + 2b - 6 = 0$ (1)