| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2006 |
| Session | January |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Factorise polynomial completely |
| Difficulty | Easy -1.2 This is a straightforward factorisation requiring only basic algebraic manipulation: factor out the common x, then factorise the resulting quadratic. It's simpler than average A-level questions as it requires no trial-and-error with the factor theorem, no problem-solving, and is a single-step process testing only basic factorisation skills. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
| Answer | Marks | Guidance |
|---|---|---|
| \(x(x^2 - 4x + 3) = x(x-3)(x-1)\) | M1, M1 A1 | Factor of \(x\) (Allow \((x-0)\)); Factorise 3 term quadratic |
$x(x^2 - 4x + 3) = x(x-3)(x-1)$ | M1, M1 A1 | Factor of $x$ (Allow $(x-0)$); Factorise 3 term quadratic
**Total: 3 marks**
---\begin{enumerate}
\item Factorise completely
\end{enumerate}
$$x ^ { 3 } - 4 x ^ { 2 } + 3 x .$$
\hfill \mbox{\textit{Edexcel C1 2006 Q1 [3]}}