| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Given factor, find all roots |
| Difficulty | Moderate -0.3 This is a straightforward application of the factor theorem requiring polynomial division and solving a quadratic. While it's Further Maths content, the question is routine: verify the given root, perform division to find the quadratic factor, then solve. The given root eliminates the problem-solving aspect, making this slightly easier than average despite being FP1. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
$$\text{f}(x) = 2x^3 - 8x^2 + 7x - 3.$$
Given that $x = 3$ is a solution of the equation f$(x) = 0$, solve f$(x) = 0$ completely.
[5]
\hfill \mbox{\textit{Edexcel FP1 Q1 [5]}}