| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Two unknowns, direct system |
| Difficulty | Moderate -0.3 This is a straightforward application of the Remainder Theorem requiring students to set up two simultaneous equations from f(3)=14 and f(-1)=-18, solve for a and b, then verify (x-2) is a factor. While it involves multiple steps and algebraic manipulation, it's a standard textbook exercise testing routine techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
f(x) = x³ + ax² + bx - 10, where a and b are constants.
When f(x) is divided by (x - 3), the remainder is 14.
When f(x) is divided by (x + 1), the remainder is -18.
\begin{enumerate}[label=(\alph*)]
\item Find the value of a and the value of b. [5]
\item Show that (x - 2) is a factor of f(x). [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q1 [7]}}