FP2 June 2008 Q2
2.
(a) Simplify the expression \(\dfrac{(x+3)(x+9)}{x-1} - (3x-5)\), giving your answer in the form \(\dfrac{a(x+b)(x+c)}{x-1}\), where \(a\), \(b\) and \(c\) are integers. (4)
(b) Hence, or otherwise, solve the inequality \[\frac{(x+3)(x+9)}{x-1} > 3x - 5\] (4)
| Scheme | Marks |
|---|---|
| Consider \(\dfrac{(x+3)(x+9) - (3x-5)(x-1)}{(x-1)}\), obtaining \(\dfrac{-2x^2 + 20x + 22}{(x-1)}\) | M1A1 |
| Factorise to obtain \(\dfrac{-2(x-11)(x+1)}{(x-1)}\). | M1A1 |
| (4) |
Notes
Second M attempt to factorise quadratic expression with 3 terms (usual rules).
Second A don’t require −2 outside but can be part of factors. B1, B1
| Scheme | Marks |
|---|---|
| Identify \(x = 1\) and their two other critical values | B1ft |
| Obtain one inequality as an answer involving at least one of their critical values | M1 |
| To obtain \(x < -1,\ 1 < x < 11\) | A1, A1 |
| (4) | |
| (8 marks) |