| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2010 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Single unknown constant |
| Difficulty | Moderate -0.8 This is a straightforward application of the factor theorem requiring substitution of x=2 to find a constant, followed by a routine remainder theorem calculation. Both parts are standard textbook exercises with no problem-solving insight needed, making it easier than average but not trivial since it requires correct algebraic manipulation across two parts. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
1 The cubic polynomial $\mathrm { f } ( x )$ is defined by $\mathrm { f } ( x ) = x ^ { 3 } + a x ^ { 2 } - a x - 14$, where $a$ is a constant.\\
(i) Given that $( x - 2 )$ is a factor of $\mathrm { f } ( x )$, find the value of $a$.\\
(ii) Using this value of $a$, find the remainder when $\mathrm { f } ( x )$ is divided by ( $x + 1$ ).
\hfill \mbox{\textit{OCR C2 2010 Q1 [5]}}