| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2012 |
| Session | Specimen |
| Marks | 5 |
| Topic | Factor & Remainder Theorem |
| Type | Fully specified polynomial: verify factor and solve |
| Difficulty | Moderate -0.8 This is a straightforward application of the factor theorem requiring substitution to verify x=2 is a root, then polynomial division to find the quadratic factor, followed by solving a simple quadratic. It's below average difficulty as it's a standard textbook exercise with clear signposting and routine techniques throughout. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
**(i)** Show $f(2) = 0$ **B1**
**(ii)** Method shown e.g. division to get quadratic **M1**
Obtain two factors or roots **A1**
$(x-2)(2x-3)(x+3)$ **A1**
$x = 2,\ \dfrac{3}{2},\ -3$ (follow through *their* factors) **B1 ft**
**Total: 5 marks**2 (i) Show that $x = 2$ is a root of the equation $2 x ^ { 3 } - x ^ { 2 } - 15 x + 18 = 0$.\\
(ii) Hence solve the equation $2 x ^ { 3 } - x ^ { 2 } - 15 x + 18 = 0$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2012 Q2 [5]}}